Two continuous random variables X and Y have a joint probability density function (PDF) [tex]fy|x(y|x) = e^{(-y)}, 0 < x < \infty, 0 < y < \infty.[/tex]
The constant c, we integrate the joint PDF over the entire xy-plane:
[tex]\int\int fxy(x,y) dxdy = 1[/tex]
Integrating with respect to x first, we get:
[tex]\int\int fxy(x,y) dxdy = c \int\int e^{(-x-y)} dxdy[/tex]
[tex]= c \int 0^\infty \int 0^\infty e^{(-x-y)} dxdy[/tex]
[tex]= c \int 0^\infty e^{(-y)} dy \int 0^\infty e^{(-x)} dx[/tex]
[tex]= c (-e^{(-y)})|0^\infty (-e^{(-x)})|0^\infty[/tex]
= c (1) (1)
= c
[tex]c = 1/\int\int e^{(-x-y)} dxdy = 1/1 = 1.[/tex]
So the joint PDF is:
[tex]fxy(x,y) = e^{(-x-y)}, 0 < x < \infty, 0 < y < \infty[/tex]
The marginal PDFs of X and Y, we integrate the joint PDF over the other variable:
[tex]fx(x) = \int fxy(x,y) dy[/tex]
[tex]= \int e^{(-x-y)} dy, 0 < x < \infty[/tex]
[tex]= e^{(-x)} \int e^{(-y)} dy[/tex]
[tex]= e^{(-x)} (-e^{(-y)})|0^\infty[/tex]
[tex]= e^{(-x)[/tex]
[tex]fy(y) = \int fxy(x,y) dx[/tex]
[tex]= \int e^{(-x-y)} dx, 0 < y < \infty[/tex]
[tex]= e^{(-y)} \int e^{(-x)} dx[/tex]
[tex]= e^{(-y)} (-e^{(-x)})|0^\infty[/tex]
[tex]= e^{(-y)[/tex]
The marginal PDF of X is [tex]fx(x) = e^{(-x)}, 0 < x < \infty[/tex], and the marginal PDF of Y is [tex]fy(y) = e^{(-y)}, 0 < y < \infty[/tex].
To find the conditional PDF of X given Y = y, we use Bayes' rule:
[tex]f(x|y) = fxy(x,y) / fy(y)[/tex]
[tex]= e^{(-x-y)} / e^{(-y)[/tex]
[tex]= e^{(-x)}, 0 < x < \infty, 0 < y < \infty[/tex]
So the conditional PDF of X given Y = y is[tex]fx|y(x|y) = e^{(-x)}, 0 < x < \infty, 0 < y < \infty.[/tex]
Similarly, to find the conditional PDF of Y given X = x, we have:
[tex]f(y|x) = fxy(x,y) / fx(x)[/tex]
[tex]= e^{(-x-y)} / e^{(-x)[/tex]
[tex]= e^{(-y)}, 0 < x < \infty, 0 < y < \infty[/tex]
The conditional PDF of Y given X = x is [tex]fy|x(y|x) = e^{(-y)}, 0 < x < \infty, 0 < y < \infty.[/tex]
For similar questions on random
https://brainly.com/question/251701
#SPJ11
Suppose the true proportion of voters in the county who support a school levy is 0.55. Consider the sampling distribution for the proportion of supporters with sample size n = 169. What is the mean of this distribution? What is the standard error of this distribution?
The mean of the distribution is 0.55, and the standard error is 0.0363.
To find the mean and standard error of the sampling distribution for the proportion of supporters with sample size n=169, we use the given true proportion (p) and the sample size (n).
1. Calculate the mean: The mean of the sampling distribution is equal to the true proportion, which is p=0.55.
2. Calculate the standard error: Use the formula SE=sqrt[p(1-p)/n]. Plug in the values: SE=sqrt[0.55(1-0.55)/169] ≈ 0.0363.
So, the mean is 0.55, and the standard error is 0.0363.
To know more about standard error click on below link:
https://brainly.com/question/30667112#
#SPJ11
11. Triangle: ABC is similar to triangle: DEC
HELPPP ASAP
Answer: i think its dec good luck
Step-by-step explanation:
l
Answer:
A
Step-by-step explanation:
angle A is opposite to angle E
write a ratio that is equvilent to x/w
The right triangles which are similar because if their same size of angle have the ratio q/s of the smaller triangle equivalent to x/z of the bigger triangle.
How to evaluate for the equivalent ratio of the triangleA ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.
For the bigger triangle;
cos α = x/z {adjacent/hypotenuse}
Also for the smaller triangle;
cos α = q/s {adjacent/hypotenuse}
Therefore by comparison, the ratio q/s of the smaller triangle is equivalent to x/z of the bigger triangle.
Read more about ratio here:https://brainly.com/question/2328454
#SPJ1
Let's consider a population of people that have a life threatening disease. Suppose 70% have healthy insurance. Of those that have health insurance, 97% seek treatment. Of those that do not have health insurance, 60% do not seek treatment. If we randomly select a person from this population that has sought out treatment, what is the probability that the person has health insurance?
The probability that the person has health insurance given that they seek treatment is 0.851, or approximately 85.1%.
We can use Bayes' theorem to solve this problem. Let's define the events as follows:
H: the person has health insurance
T: the person seeks treatment
We are given:
P(H) = 0.70 (70% have health insurance)
P(T|H) = 0.97 (of those with health insurance, 97% seek treatment)
P(not T|not H) = 0.60 (of those without health insurance, 60% do not seek treatment)
We want to find P(H|T), the probability that the person has health insurance given that they seek treatment.
By Bayes' theorem:
P(H|T) = P(T|H) * P(H) / P(T)
To find P(T), we need to use the law of total probability:
P(T) = P(T|H) * P(H) + P(T|not H) * P(not H)
We are not given P(T|not H) directly, but we can find it using the complement rule:
P(T|not H) = 1 - P(not T|not H) = 1 - 0.60 = 0.40
Now we can substitute into the formula for P(T) and then into Bayes' theorem:
P(T) = P(T|H) * P(H) + P(T|not H) * P(not H) = 0.97 * 0.70 + 0.40 * 0.30 = 0.799
P(H|T) = P(T|H) * P(H) / P(T) = 0.97 * 0.70 / 0.799 = 0.851
Therefore, the probability that the person has health insurance given that they seek treatment is 0.851, or approximately 85.1%.
To learn more about treatment visit:
https://brainly.com/question/3186782
#SPJ11
find at least 10 partial sums of the series. graph both the sequence of terms and the sequence of partial sums on the same screen. does it appear that the series is convergent or divergent? if it is convergent, find the sum. if it is divergent, explain why. 1/n^2 1
The given series 1/n² is convergent, and its sum is π²/6.
The terms of the series are given by 1/n², where n is the index of the term. To find the partial sums of the series, we can add up the first n terms of the series. The partial sum S_n can be expressed as:
S_n = 1/1² + 1/2² + 1/3² + … + 1/n²
We can now calculate the first few partial sums to graph them:
S_1 = 1/1² = 1
S_2 = 1/1² + 1/2² = 1 + 1/4 = 5/4
S_3 = 1/1² + 1/2² + 1/3² = 5/4 + 1/9 ≈ 1.3611
S_4 = 1/1² + 1/2² + 1/3² + 1/4² ≈ 1.4236
Continuing this pattern, we can calculate more partial sums. Now, let's graph both the sequence of terms and the sequence of partial sums on the same screen.
Based on the graph, we can see that as n increases, the partial sums S_n approach a finite value, and they do not diverge to infinity. This suggests that the series 1/n² is convergent.
To find the sum of the series, we can take the limit of the partial sums as n approaches infinity:
lim(n->∞) S_n = lim(n->∞) (1/1² + 1/2² + 1/3² + … + 1/n²)
Using the formula for the sum of the squares of reciprocals, which is π²/6, we can conclude that:
lim(n->∞) S_n = π²/6
Therefore, the given series 1/n² is convergent, and its sum is π²/6.
To learn more about convergent here:
brainly.com/question/15415793#
#SPJ11
the ratio of the surface areas of two similar cylinders is 4/25. the radius of the circular base of the larger cylinder is 0.5 centimeters. what is the radius of the circular base of the smaller cylinder? drag a value to the box to correctly complete the statement.
Answer:
.2 Cm
Step-by-step explanation:
The harmonic series is introduced in sequences and series testsconcepts.. Demonstrate that it diverges with 2 different tests.
The harmonic series diverges with two different tests namely divergence test and comparison test.
Using the formula of harmonic test -
Hn = 1 + 1/2 + 1/3 + 1/4 + ... + 1/n
where n is a number that is positive and bigger than 1. The harmonic series is a well-known illustration of a divergent series, which lacks a finite sum. We can see that for the harmonic series, the terms 1/n do not move closer to zero as n increases. In reality, 1/n approaches 0, but never truly achieves it, as n approaches infinity.
Whereas, as per comparison test, if two series, Σan and Σbn, are such that for every n, 0 < a_n <b_n, and b_n converges, then Σan must likewise converge. On the other hand, if b_n diverges, Σan must likewise diverge. The harmonic series with another series can be compared to apply the comparison test to it. Using the p-series test with p = 2, we may determine that the series 1/n² converges.
Read more about harmonic series on:
https://brainly.com/question/22076584
#SPJ4
Given that lim x→a f(x) = 0, lim x→a g(x) = 0, lim x→a h(x) = 1, lim x→a p(x) = [infinity], lim x→a q(x) = 0. Which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible. Enter I to indicate an indeterminate form, INF for positive infinity, NINF for negative infinity, and D for the limit does not exist or we don't have enough information to determine the limit. f(x) (a) lim x+ f(x) / g(x) = (b) lim x→a f(x) /p(x) =(c) lim x→a p(x) /h(x) =(d) lim x→a p(x) / f(x) =(e) lim lim x→a p(x) / q(x) =
(a) lim x→a f(x) / g(x) = I
(b) lim x→a f(x) / p(x) = 0
(c) lim x→a p(x) / h(x) = INF
(d) lim x→a p(x) / f(x) = INF
(e) lim x→a p(x) / q(x) = INF
(a) Both f(x) and g(x) approach 0, resulting in the indeterminate form 0/0.
(b) f(x) approaches 0 while p(x) approaches infinity, leading to a limit of 0.
(c) p(x) approaches infinity while h(x) approaches 1, so the limit is positive infinity.
(d) p(x) approaches infinity while f(x) approaches 0, resulting in a limit of positive infinity.
(e) p(x) approaches infinity and q(x) approaches 0, leading to a limit of positive infinity.
To know more about indeterminate form click on below link:
https://brainly.com/question/30640456#
#SPJ11
We can control the size of FWER by choosing significance levels of the individual tests to vary with the size of the series of tests. In practice, this translates to correcting p-values before comparing with a fixed significance level e.g. a = 0.05. Bonferroni Correction In a series of m tests, if the significance level of each test is set to a/m, or equivalently if the null hypothesis H, of each test i is rejected when the corresponding p-value is bounded by: a pi m then FWER
In multiple testing situations, it's important to control the family-wise error rate (FWER) to avoid making false conclusions. If the p-value is below the adjusted significance level, we reject the null hypothesis for that test. Overall, the Bonferroni Correction is a useful tool for controlling FWER in multiple testing situations, and can help ensure that our conclusions are reliable and accurate.
Explanation of the terms "significance," "Bonferroni Correction," and "null hypothesis," and how they relate to controlling the Family-Wise Error Rate (FWER) in a series of tests. Here's a concise explanation:
1. Significance: Significance is the probability of rejecting the null hypothesis when it is true. In hypothesis testing, it is denoted by the Greek letter alpha (α), which is the significance level. A common value used for α is 0.05, meaning there's a 5% chance of rejecting the null hypothesis when it's true.
2. Null Hypothesis (H0): The null hypothesis is the statement being tested in a hypothesis test. It is usually a claim about a population parameter, such as a mean or proportion, and assumes that there is no effect or difference between groups being compared.
3. Bonferroni Correction: The Bonferroni Correction is a method used to control the FWER when performing multiple hypothesis tests. It adjusts the significance level (α) by dividing it by the number of tests (m) conducted, i.e., α/m.
To control the FWER, we can use the Bonferroni Correction by setting the significance level of each individual test to α/m. We then reject the null hypothesis (H0) of each test (i) when the corresponding p-value is less than or equal to the adjusted significance level, which is α * pi ≤ m. This ensures that the overall FWER is controlled at the desired level (e.g., α = 0.05).
Learn more about Bonferroni Correction here: brainly.com/question/3487014
#SPJ11
Assume that the recursively defined sequence converges and find its limit. a1 = -42, an+1 = √42+ anThe sequence converges to ___ (Type an integer or a decimal.)
The sequence converges to 7.
To find the limit of the sequence, we can start by finding a pattern among its terms:
a1 = -42
a2 = √(42 + (-42)) = 0
a3 = √(42 + 0) = √42
a4 = √(42 + √42)
a5 = √(42 + √(42 + √42))
...
As n approaches infinity, the expression under the square root sign
becomes less and less important compared to the term being added to it (which is always 42).
Therefore, we can assume that the limit of the sequence, if it exists, will satisfy the equation:
L = √(42 + L)
Solving for L, we get:
[tex]L^2 = 42 + L\\L^2 - L - 42 = 0[/tex]
(L - 7)(L + 6) = 0
Since the sequence starts with a1 = -42, the limit must be non-negative, so the only possible limit is L = 7.
for such more question on sequence converges
https://brainly.com/question/11354790
#SPJ11
Solutions to a separable ODE can 'go missing' when both sides of the ODE are divided by a function of y.
Yes, it is possible for solutions to a separable ODE to "go missing" when both sides of the ODE are divided by a function of y.
When we have a separable ODE of the form
g(y) dy/dx = f(x)
we can integrate both sides with respect to their respective variables to obtain
∫ g(y) dy = ∫ f(x) dx
However, to perform this integration, we need to assume that g(y) is nonzero for all values of y in the domain of the solution. If g(y) has any zeros in the domain, then we need to treat those zeros as singularities and solve the ODE separately on each side of the singularity.
If we divide both sides of the ODE by a function of y, say h(y), to obtain
dy/dx = f(x)/h(y)
then we need to be careful to ensure that h(y) is nonzero for all y in the domain of the solution. If h(y) has any zeros in the domain, then dividing by h(y) can cause solutions to "go missing" at those points. This is because dividing by zero is undefined, and solutions can become singular or undefined at those points.
For example, consider the separable ODE
y' = 2x/(y-1)
which we can rewrite as
(y-1) y' = 2x
Dividing both sides by y-1, we get
y' = 2x/(y-1)
which is the same as the original ODE. However, this division by y-1 is not valid when y=1, since it makes the denominator zero. At y=1, the original ODE has a singularity, and we need to treat this point separately when finding the solution. If we fail to do so, we may miss a solution that exists only at y=1.
To learn more about separable visit:
https://brainly.com/question/16774902
#SPJ11
4. Conditional probability cannot be used for more than two events. True or False?
False. Conditional probability can be used for more than two events.
In fact, conditional chance is a essential concept in opportunity idea this is used to calculate the opportunity of an event A given that event B has befell.
This idea may be extended to more than one events, where the chance of an event A given that occasions B and C have came about can be calculated the use of the formula P(A|B,C) = P(A,B,C)/P(B,C).
Wherein P(A,B,C) is the joint possibility of activities A, B, and C happening together, and P(B,C) is the opportunity of activities B and C occurring together. This system can be prolonged to any variety of occasions, making conditional possibility a effective device in chance theory and information.
Learn more about probability:-
https://brainly.com/question/13604758
#SPJ4
Use the box plots below to make comparisons
Number line labeled Number of insects identified with two box plots above it. Box plot labeled First trip has points at 2, 16, 17, 20, and 22. A box extends from 16 to 20 with a vertical line through 17. Lines extend from 16 to 2 and from 20 to 22. Box plot labeled Second trip has points at 15, 18, 19, 20, and 22. A box extends from 18 to 20 with a vertical line through 19. Lines extend from 18 to 15 and from 20 to 22.
Question 6 options:
The range of the first trip is smaller than the range of the second trip
The median of the second trip is higher than the median of the first trip
The interquartile range (IQR) of the second trip is larger than the IQR of the first trip
The first trip and the second trip have different maximum values
For the given box plot: The median of the second trip is higher than the median of the first trip.
What are box plots?Box plots, often called box-and-whisker plots, are graphical representations of data sets that highlight essential characteristics and summarise the distribution of the data. A box plot consists of a rectangle (the box) that spans the middle value of the data from the lower quartile (Q1) to the upper quartile (Q3), and a vertical line (the median) inside the box. Any data points outside of this range are displayed as separate dots (outliers), and whiskers (lines) extend from the box to the lowest and highest data points within 1.5 times the IQR (interquartile range). Box plots make it simple to compare several sets of data, and they can highlight variations in central tendency, variability, and skewness.
From the description of the box plots we observe that:
The first trip's range is greater than the second trip's range because the first trip's whiskers are longer than the second trip's whiskers.
Due to the second trip's box being relocated to the right of the first trip's box, the median of the second trip is greater than the median of the first.
Because the box for the first trip is wider than the box for the second trip, the interquartile range (IQR) of the second trip is less than the IQR of the first trip.
Since both trips have a data point at 22, they both have the same highest value.
Hence, The median of the second trip is higher than the median of the first trip.
Learn more about box plots here:
https://brainly.com/question/1523909
#SPJ1
The population of Log Village is 1800 in 2010 and the population increases each year by 9%. Which equation can be used to determine the population, y, of Log Village x years after 2010? a)y=0.09(1800)^x b)y=1800 (1.09)^x c)y=1800(0.91)^x d)y = 1800(.09)^x
Answer:
B) [tex]y=1800(1.09)^{x}[/tex]
Step-by-step explanation:
The initial value (1800) is outside the parenthesis
The rate (+1 because it's growth not decay) goes inside the parenthesis
The exponent is the time (x)
Answer: I took the test
Step-by-step explanation:
each character in a password is either a digit [0-9] or lowercase letter [a-z]. how many valid passwords are there with the given restriction(s)?
There are 36 possible characters for each position in the password, consisting of 10 digits and 26 lowercase letters. Therefore, there are
[tex]36^N[/tex]
possible passwords with N characters.
For a password of length 1, there are 36 possible passwords. For a password of length 2, there are 1,296 possible passwords. For a password of length 3, there are 46,656 possible passwords, and so on.
Since each character in the password can only be a digit or lowercase letter, we must subtract the number of passwords that do not meet this criteria. For example, a password containing an uppercase letter, a symbol, or a whitespace character would not be valid.
The number of valid passwords is simply
[tex]36^N[/tex]
minus the number of invalid passwords. The exact number of invalid passwords depends on the length of the password and the number of positions where an invalid character could be placed.
The total number of valid passwords can be calculated as follows:
Valid passwords =
[tex]36^N[/tex] - number of invalid passwords.
Learn more about passwords here:
https://brainly.com/question/23249667
#SPJ4
Is the following a statistical question?
How many siblings does a typical student at your school have?
yes or no?
Answer: yes
Step-by-step explanation:
you could do that one and also you could do Which classroom in your school has the most books?
Two functions in F(S, F) are equal if and only if they have the same value at each element of S. true or false
The statement 'two functions in F(S, F) are equal if and only if they have the same value at each element of S' is true as functions are considered equal when their domain (S) and co-domain (F) are the same, and they produce the same output values for each input element in their domain.
If two functions in F(S, F) have the same value at each element of S, then they are equal. This is because a function maps each element of the domain (S) to a unique element of the range (F). Therefore, if two functions have the same output for every input, then they are mapping each element of S to the same corresponding element in F, which means that they are the same function.
Conversely, if two functions are equal, then they have the same value at each element of S, since a function's value is uniquely determined by its input.
To learn more about functions, click here:
https://brainly.com/question/12431044
#SPJ11
What are strata? Which sampling approach includes strata ?
Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members’ shared attributes or characteristics, such as income or educational attainment. Stratified random sampling has numerous applications and benefits, such as studying population demographics and life expectancy.
Stratified random sampling is also called proportional random sampling or quota random sampling.
SOMEONE HELP ME OUT!!
There are 6 parts that correspond to these numbers, so the probability of getting a number less than 7 is 6/8 or 3/4.
So, the correct answer is option (a) 3/4.
What is meant by likelihood?According to the knowledge or evidence that is currently available, likelihood describes the possibility or probability of an occurrence or result occurring.
When describing the likelihood of an outcome given a collection of observable facts or information, it is frequently employed in statistics.
The likelihood in statistical analysis is frequently described as a probability distribution or function, which expresses the possibility of a certain collection of data given a particular set of assumptions or characteristics.
A statistical model's unknown parameters, such as the mean and variance of a normal distribution or the odds ratio of a logistic regression model, are estimated using the likelihood function.
Since the spinner is divided into 8 equal parts and we want to find the probability of getting a number less than 7, we need to count the number of parts that correspond to numbers less than 7, which are 1, 2, 3, 4, 5, and 6.
These numbers are divided into 6 parts, hence the likelihood of receiving a result that is less than 7 is 6/8 or 3/4.
The solution is therefore (a) 3/4.
To know more about statistical analysis visit:
https://brainly.com/question/14724376
#SPJ1
One may wonder if people of similar heights tend to marry each other. For this purpose, a sample of newly married couples was selected. Let X be the height of the husband and Y be the height of the wife. The heights (in centimeters) of husbands and wives are found in Table 2.11. The data can also be found at the book's Website. (e) What would the correlation be if every man married a woman exactly 5 centimeters shorter than him?
On solving the provided query we have As a result, in the given sample, there is a 0.861 correlation between the heights of the husbands and wives.
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
The sample correlation coefficient formula may be used to determine the correlation between X and Y in the given sample:
r is equal to (nXY - XY) / sqrt((nX2 - (X)2)(nY2 - (Y)2)
where n is the sample size, XY is the product of X and Y's sum, X and Y's sums, X and Y's square sums, and X and Y's square sums are all present.
We may get the sample correlation coefficient by using the information in Table 2.11 as follows:
n = 10
r = (10296510 - 17491602) / sqrt((10313821 - 1749^2)(10*282852 - 1602^2))
= 0.861
As a result, in the given sample, there is a 0.861 correlation between the heights of the husbands and wives.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Nutrients in low concentrations inhibit growth of an organism, but high concentrations are often toxic. Let c be the concentration of a particular nutrient (in moles/liter) and P be the population density of an organism (in number/cm2). Suppose that it is found that the effect of this nutrient causes the population to grow according to the equation: 100c 1 + 2500c2 P(c) = . Find the concentration of the nutrient that yields the largest population density of this organism and what the population density of this organism is at this optimal concentration. Optimal nutrient concentration = Largest population density
The concentration of the nutrient that yields the largest population density of this organism is c ≈ (1/5000)^(1/3) moles/liter. The population density of this organism is at this optimal concentration is P(c) ≈ 0.9772 number/cm².
To find the optimal nutrient concentration that yields the largest population density, we need to analyze the given equation:
P(c) = 100c / (1 + 2500c²)
To maximize the population density P(c), we can find the critical points by taking the first derivative of P(c) with respect to the concentration c, and then setting it equal to 0.
P'(c) = dP(c)/dc
Using the Quotient Rule, the first derivative is:
P'(c) = ( (1 + 2500c²) * (100) - 100c * (5000c) ) / (1 + 2500c²)²
Simplify the expression:
P'(c) = (100 - 500000c³) / (1 + 2500c²)²
Now, set P'(c) = 0 to find the critical points:
0 = (100 - 500000c³) / (1 + 2500c²)²
Since the denominator can't be equal to zero, we focus on the numerator:
100 - 500000c³ = 0
Rearrange the equation to solve for c:
500000c³ = 100
c³ = 100 / 500000
c³ = 1 / 5000
c = (1/5000)^(1/3)
Now, we can find the population density at this optimal concentration:
P(c) = 100 * (1/5000)^(1/3) / (1 + 2500 * (1/5000)^(2/3))
P(c) ≈ 0.9772 (in number/cm²)
So, the optimal nutrient concentration is approximately c ≈ (1/5000)^(1/3) moles/liter, which yields the largest population density of approximately P(c) ≈ 0.9772 number/cm².
To learn more about population density, click here:
https://brainly.com/question/1581160
#SPJ11
2. The Attributional Complexity Scale (Fletcher et al., 1986) is a 28 item Likert-scored measure. Responses range from 1 (Disagree Strongly) to 7 (Agree Strongly). Items include: "I believe it is important to analyze and understand our own thinking process;" "I think a lot about the influence that I have on other people's behavior;" "I have thought a lot about the family background and the personal history of people who are close to me, in order to understand why they are the sort of people they are." High scores mean greater complex thinking; low scores mean less complex thinking. Professor Kinon believes that on average people administered the Attributional Complexity Scale will score above the midpoint; the midpoint being 4. Is Professor Kinon right? (Total = 38 points) Participant Attributional Complexity (x) I 1 2 3 4 5 6 7 5.54 5.32 4.96 5.64 5.50 5.86 6.11 4.89 4.36 8 9 M=5.35 SD=0.54 a. State the null as well as the alternative hypothesis. Be sure to include symbols as well as words. (6 points)
Null Hypothesis is 4 and Alternative Hypothesis is greater than 34.
Let's first state the null hypothesis (H0) and the alternative hypothesis (Ha) using the information given.
Null Hypothesis (H0): The average score on the Attributional Complexity Scale is equal to the midpoint (4). In symbols, this can be written as H0: μ = 4.
Alternative Hypothesis (Ha): The average score on the Attributional Complexity Scale is greater than the midpoint (4). In symbols, this can be written as Ha: μ > 4.
Now, let's analyze the data provided:
- The sample mean (M) is 5.35
- The sample standard deviation (SD) is 0.54
- The sample size (n) is 9 (since there are 9 participants)
To test the hypothesis, you would typically perform a one-sample t-test, comparing the sample mean to the midpoint of 4. Based on the given information, the sample mean is higher than the midpoint (5.35 > 4), which supports the alternative hypothesis that people, on average, score above the midpoint on the Attributional Complexity Scale. However, to draw a valid conclusion, you would need to calculate the t-value, degrees of freedom, and compare the result to the critical value or obtain a p-value to determine the statistical significance of the findings.
Learn more about null hypothesis here:
https://brainly.com/question/30665946
#SPJ11
Suppose x is a uniform random variable with c=10 and d=70. Find the probability that a randomly selected observation is between 13 and 65. a) 0.133 b) 0.867 c) 0.8 d) 0.5
The probability that a randomly selected observation is between 13 and 65 is 0.867. Therefore, the correct option is B.
We are required to determine the probability that a randomly selected observation of the uniform random variable x is between 13 and 65 with c = 10 and d = 70.
In order to calculate the probability, follow these steps:1. Calculate the range of the variable: d -
c = 70 - 10 = 60
2. Calculate the length of the interval of interest:
65 - 13 = 52
3. Divide the length of the interval of interest by the range of the variable:
52 / 60 = 0.867
So, the probability that a randomly selected observation of the uniform variable x lies between 13 and 65 is 0.867, which corresponds to option B.
Learn more about Probability:
https://brainly.com/question/25839839
#SPJ11
a b as 2. Find the volume of the parallelepiped having a = (1,4,7), D = (2,-1,4) and C = c =(0,–9,18) adjacent edges. What conclusion can you make about vector a, b and c?
The volume of the parallelepiped having edges a, b, and c is 300 cubic units. Scalar triple product is negative for these vectors.
The volume of a parallelepiped is given by the scalar triple product of its adjacent edges. So, to find the volume of the parallelepiped having edges a, b, and c, we need to calculate the scalar triple product of these vectors:
V = |a · (b x c)|
where · represents the dot product and x represents the cross product of vectors.
First, we need to find the cross product of b and c:
b x c = [(-1)(18) - (4)(-9), (4)(0) - (2)(18), (2)(-9) - (-1)(0)]
= [-30, -36, -18]
Next, we take the dot product of a and this cross product:
a · (b x c) = (1)(-30) + (4)(-36) + (7)(-18)
= -30 - 144 - 126
= -300
Finally, we take the absolute value of this scalar triple product to get the volume of the parallelepiped:
V = |-300| = 300 cubic units
As for the conclusion about vectors a, b, and c, we can observe that the scalar triple product is negative, which indicates that the orientation of the parallelepiped is opposite to that of the coordinate system. This means that the three vectors do not form a right-handed set of vectors, as is typically assumed. Instead, they form a left-handed set of vectors.
To learn more about volume click on,
https://brainly.com/question/31400571
#SPJ4
each year, a company either makes a profit or takes a loss. if the company made a profit the year before, they will make a profit with probability 0.8. if they took a loss the year before, they will make a profit with probability 0.2. what is the long-run probability the company will make a profit?g
Answer:
The long-run probability that the company will make a profit is 0.5, or 50%.
Step-by-step explanation:
The long-run probability of the company making a profit can be found using the concept of a steady-state probability.
Let P(P) be the long-run probability of making a profit, and P(L) be the long-run probability of taking a loss.
According to the given information:
1. If the company made a profit the year before, they make a profit with probability 0.8.
2. If they took a loss the year before, they make a profit with probability 0.2.
Using these probabilities, we can set up the following system of equations:
P(P) = 0.8 * P(P) + 0.2 * P(L)
P(L) = 1 - P(P)
Now we can substitute the second equation into the first equation to solve for P(P):
P(P) = 0.8 * P(P) + 0.2 * (1 - P(P))
To solve for P(P), we can rearrange the equation:
P(P) - 0.8 * P(P) = 0.2 - 0.2 * P(P)
Combining terms gives:
0.2 * P(P) = 0.2 - 0.2 * P(P)
Dividing by 0.2 gives:
P(P) = 1 - P(P)
Adding P(P) to both sides:
2 * P(P) = 1
Finally, dividing by 2:
P(P) = 0.5
So, the long-run probability that the company will make a profit is 0.5, or 50%.
learn more about "Probability":-https://brainly.com/question/251701
#SPJ11
describe what it means if the margin of error for a 95% confidence interval for apopulation parameter equals 0.13
If the margin of error for a 95% confidence interval for a population parameter equals 0.13, it means that we can be 95% confident that the true value of the population parameter lies within a range that extends 0.13 units in either direction from the point estimate.
A confidence interval is a range of values within which we estimate the true value of a population parameter with a certain level of confidence. The margin of error is the amount by which the estimate is likely to deviate from the true population value. In this case, the margin of error is 0.13.
A 95% confidence interval means that if we were to take multiple samples from the same population and construct confidence intervals for each sample using the same method, 95% of those intervals would contain the true population parameter. In other words, there is a 95% chance that the true value of the population parameter falls within the calculated confidence interval.
The margin of error of 0.13 indicates the width of the confidence interval. It represents the maximum amount by which the point estimate, which is the center of the confidence interval, can deviate from the true population value. The confidence interval will extend 0.13 units in both directions from the point estimate.
Therefore, if the margin of error for a 95% confidence interval for a population parameter equals 0.13, it means that we can be 95% confident that the true value of the population parameter lies within a range that extends 0.13 units in either direction from the point estimate
To learn more about confidence interval here:
brainly.com/question/24131141#
#SPJ11
Marian went shopping for shirts and pants today. If he bought five shirts that each cost $15 and four pairs of pants which each cost $10 how much money in total did he spend
Answer:
$115
Step-by-step explanation:
shirt: $15 each
pants: $10 each
5 shirts + 4 pants =
= 5 × $15 + 4 × $10
= $75 + $40
= $115
Answer: $115
QUESTION 11 You create a 99% CI for M - 22 from a sample of size N = 15, your CI is 10 to 34. What will happen to the size of your Cl if you change it to a 95% CI Widen it Narrow
If you change the confidence level from 99% to 95%, the size of the confidence interval will become smaller. Therefore, we can see that the size of the confidence interval has been reduced from 24 (10 to 34) to 22.26 (10.87 to 33.13) when we change from a 99% CI to a 95% CI.
To see why, let's first calculate the margin of error for the 99% CI:
Margin of error = (upper bound - lower bound) / 2 = (34 - 10) / 2 = 12
The point estimate for M is M - 22, so the 99% confidence interval can be written as:
M - 22 ± 12
To calculate a 95% confidence interval, we need to find the z-score for the 97.5th percentile of the standard normal distribution, which is 1.96. Using this value, the margin of error for the 95% CI can be calculated as:
Margin of error = 1.96 * standard error
where the standard error is the standard deviation of the sample divided by the square root of the sample size:
standard error = s / sqrt(N)
We do not have the standard deviation of the sample, so we cannot calculate the standard error. However, we can make an assumption that the standard deviation of the population is equal to the standard deviation of the sample. Using the given 99% CI, we can estimate the standard deviation of the sample as:
12 = 2.58 * s / sqrt(15)
Solving for s, we get:
s = 14.14
Using this value for s, we can calculate the margin of error for the 95% CI as:
Margin of error = 1.96 * s / sqrt(N) = 1.96 * 14.14 / sqrt(15) ≈ 9.13
So the 95% CI is:
M - 22 ± 9.13 = 10.87 to 33.13
Learn more about Margin of error here:
https://brainly.com/question/30633768
#SPJ11
when two variables are correlated, can the researcher be sure that one variable causes the other? why or why not?
When two variables are correlated, it means that there is a statistical relationship between them. However, correlation does not necessarily imply causation.
In other words, just because two variables are correlated does not mean that one variable causes the other. There may be other factors or variables that contribute to the relationship between the two variables. To establish causation, a researcher would need to conduct further studies to rule out any confounding variables and establish a clear temporal sequence between the variables. Therefore, researchers cannot be completely sure that one variable causes the other simply based on correlation. A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables.
Learn more about variables here, https://brainly.com/question/25223322
#SPJ11
what is the surface area of the wood?answer options with 5 optionsa.48 inches squaredb.68 inches squaredc.96 inches squaredd.100 inches squarede.108 inches squared
The surface area of the wood Cannot be determined.
However, even with the answer options given, it is not possible to determine the surface area of the wood without additional information. The surface area of a piece of wood depends on its dimensions and shape, and the answer options given do not provide any information about these factors.
For example, a rectangular piece of wood with dimensions 4 inches by 3 inches by 4 inches would have a surface area of 52 square inches, which is not among the answer options provided. On the other hand, a cube-shaped piece of wood with dimensions 3 inches by 3 inches by 3 inches would have a surface area of 54 square inches, which is also not among the answer options provided.
Therefore, the correct answer is still "Cannot be determined".
To learn more about dimensions visit:
https://brainly.com/question/29581656
#SPJ11
