a courtroom spectator merely looks at the defendant and says, “He’s guilty, i tell you.”

Answer:

[tex]\dfrac{1}{10}[/tex]

Step-by-step explanation:

Probability of the captain hitting the pirate ship [tex]=\dfrac{1}{2}[/tex]

Probability of the pirate hitting the captain's ship [tex]=\dfrac{1}{5}[/tex]

If both fire cannons at the same time, the probability that both the pirate and the captain hit each other's ship

=P(Captain Hits AND Pirate Hits)

=P(Captain Hits) X P(Pirate Hits)

[tex]=\dfrac{1}{2} X \dfrac{1}{5}\\\\=\dfrac{1}{10}[/tex]

Answer:

The recoil velocity of the gun is [tex]0.72\,\,\frac{km}{h}[/tex]  and is pointing in opposite direction to the velocity of the bullet.

Step-by-step explanation:

Use conservation of linear momentum, which states that the momentum of the bullet (product of the bullet's mass times its speed) should equal in absolute value the momentum of the recoiling gun (its mass times its recoil velocity).

We also write the mass of the bullet in the same units as the mass of the gun (for example kilograms). Mass of the bullet = 0.010 kg

In mathematical terms, we have:

[tex]5\, kg * v= 0.01 \,kg\,* 360\,\frac{km}{h} \\v=\frac{0.01\,*360}{5} \,\,\frac{km}{h}\\v=0.72\,\,\frac{km}{h}[/tex]

Answer:

10000

Step-by-step explanation:

3.34x=33400

x=10000

The number is x=10000.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

let, the number = x

now, we get,

3.34x=33400

x=10000

Hence, The number is x=10000.

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===========================================================

Explanation:

Start at the point (0,0) which is the origin. Move up 2 units then to the right 3 units to arrive at the next blue point (3,2). We see that

rise = 2

run = 3

slope = rise/run = 2/3

----------

If you want to use the slope formula, then you would say

m = (y2 - y1)/(x2 - x1)

m = (2 - 0)/(3 - 0)

m = 2/3

I used the two points (0,0) and (3,2). You could use any two points you like on this line.

Side note: The slope is positive because we are moving uphill as you move from left to right along this orange line.

The slope of the line p is given by 2/3.

The tangent value of the angle which the straight line makes with the positive X axis is called the slope of that particular straight line.

If s line passes through two points (a,b) and (c,d) then the slope of the line (m) is given by,

m = (d-b)/(c-a)

Here in the given figure we can see that the given line p passes through (3,2), (-3,-2) and the origin (0,0)

then taking any two points out of that three (3,2), (0,0) we get, the slope of p is given by,

m = (2-0)/(3-0) = 2/3

Hence slope of line p is given by 2/3.

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Answer:

11453

Step-by-step explanation:

Answer:

A. Observational study

Step-by-step explanation:

In research, an observational study is a type of study in which the researcher observes a phenomenon and tries to establish some relationship between the different variables he/she is observing. In other words, the researcher only observes and doesn't give a treatment.

On the other hand, when we have a experiment, we usually have 2 different groups (one that will receive a treatment and one who won't) and the researcher compares the differences between these two groups because of the treatment. In other words, the researcher does something other than just observing.

In this example, the research is going to determine if there is a relation between hearing loss and exposure to mumps. In this example the researcher is only going to observe how people who have been exposed to mumps are regarding hearing loss (we can say this since it will be unethical for example for the researcher to create an experiment in which he/she exposes a group to mumps). Therefore, he is going to observe how the past exposure to mumps could be related with the hearing loss.

Thus, this is an observational study.

Answer: There is a 0.88% chance of pulling three red marbles in a row.

Step-by-step explanation:

First pull = 4/15 (26.67%)

second pull = 3/14 (21.43%)

Third pull = 2/13 (15.38%)

You need to multiply these three fractions to get the probability of pulling three reds in a row, doing that will get you 4/455 or 0.88%

Answer:

The p-value obtained is less than the significance level at which the test was performed at, hence, we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.

Step-by-step explanation:

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful

Mathematically,

The null hypothesis is represented as

H₀: p = 0

The alternative hypothesis is represented as

Hₐ: p > 0

To do this test, we will use the z-distribution because although no information on the population standard deviation is known, the sample size is large enough.

So, we compute the test statistic

z = (x - μ)/σₓ

x = sample proportion = (31/3000) = 0.0103

μ = p₀ = 0

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 3000

σₓ = √[0.0103×0.9897/3000] = 0.0018462936 = 0.0018463

z = (0.0103 - 0) ÷ 0.0018463

z = 5.60

checking the tables for the p-value of this test statistic

Significance level = 1% = 0.01

The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for z = 5.60, at 0.01 significance level, with a one tailed condition) = < 0.00001

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.01

p-value = < 0.00001

p-value < 0.00001 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.

Hope this Helps!!!

.

2.

.

I hope it helps you

Answer:

d = 61.25 m

Step-by-step explanation:

The number of seconds, t it takes for an object to fall a distance of d meters can be found using the formula :

[tex]t=2\sqrt{\dfrac{d}{g}}[/tex] .....(1)

It is required to find the distance covered by ab object in 5 seconds

Solving equation (1) for d. So,

[tex]d=\dfrac{t^2g}{4}[/tex]

Putting all the values we get :

[tex]d=\dfrac{(5)^2\times 9.8}{4}\\\\d=61.25\ m[/tex]

So, the distance covered by the object is 61.25 m.

The object will fall at a distance of 122.5 meters.

Acceleration is the rate of change of velocity with time, both in terms of speed and direction.

Given that, t = √(2d/g).

t = √(2d/g

t√(g/2) = √d

t²(g/2) = d

Or, d = t²(g/2)

Substitute g = 9.8 and t = 5:

d = 5²(9.8/2)

d = 122.5 meters

Hence, the object will fall at a distance of 122.5 meters.

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Answer:

Step-by-step explanation:

The measure of an arc is twice the measure of the inscribed angle that subtends that arc. A tangent is a special case where the chord that is one leg of the inscribed angle has a length of zero.

1. Short arc LJ is 2a°. Short arc LK is 2b°. Then arc JLK is 2(a+b)°, and short arc JK is ...

  arc JK = 360° -2(a +b)° . . . . . matches choice B

__

2. Long arc WY is twice the measure of "inscribed" angle WYZ, so is ...

  long ard WY = 2(104°) = 208°

Then short arc WY is ...

  arc WXY = 360° -208° = 152°

__

3. The arc measures are double those of the corresponding inscribed angles. We can add up the arcs around the circle:

  (arc AB +arc BC) = 2×70° = 140° . . . inscribed angle relation

  (arc BC +arc CD) = 2×98° = 196° . . . inscribed angle relation

  arc AB + arc BC +arc CD +arc DA = 360° . . . . sum around the circle

Adding the first two equations with arc DA, we have ...

  (arc AB + arc BC) +(arc BC +arc CD) +arc DA = 360° +arc BC

  140° +196° +80° = 360° +arc BC

  416° -360° = arc BC = 56° . . . . . matches choice B

__

4. Angle C and angle A are supplementary in this inscribed quadrilateral.

  angle C = 180° -98° = 82° . . . . . matches choice A

Answer:

a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

b) We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]  

d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Step-by-step explanation:

Information provided

[tex]\bar X=23400[/tex] represent the sample mean

[tex]s=1412[/tex] represent the sample standard deviation

[tex]n=18[/tex] sample size  

[tex]\mu_o =22100[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Part a

We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

Part b

We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

Part c

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]    

Part d

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Answer:

0.4929 = 49.29% probability that he voted in favor of Scott Walker

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Having a college degree.

Event B: Voting for Scott Walker.

They found that 57% of the respondents voted in favor of Scott Walker.

This means that [tex]P(B) = 0.57[/tex]

Additionally, they estimated that of those who did vote in favor for Scott Walker, 33% had a college degree

This means that [tex]P(A|B) = 0.33[/tex]

Probability of having a college degree.

33% of those who voted for Scott Walker(57%).

45% of those who voted against Scott Walker(100 - 57 = 43%). So

[tex]P(A) = 0.33*0.57 + 0.45*0.43 = 0.3816[/tex]

What is the probability that he voted in favor of Scott Walker?

[tex]P(B|A) = \frac{0.57*0.33}{0.3816} = 0.4929[/tex]

0.4929 = 49.29% probability that he voted in favor of Scott Walker

Answer:

y=-5/2x-1

Step-by-step explanation:

first find the gradient whereas since the two lines are parallel they hav the same gradient. y=mx+c whereas m is the gradient. 5x+2y=12

2y=-5x+12

y=-5/2x+12(so the gradient is -5/2x..... gradient=-5/2

y-4=-5/2

x+2

y-4=-5/2(x+2)

y-4=-5/2x-5

y=-5/2x-5+4

y=-5/2x-1

The equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4) is y = -5/2 x - 1.

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

Given that the equation of the line is,

5x + 2y = 12

2y = -5x + 12

y = -5/2 x + 6

This is in the slope intercept form, where the slope = -5/2.

Slopes of two parallel lines are equal.

So any line parallel to the given line will be of the form y = -5/2 x + c

Given line passes through (-2, 4).

Substituting (-2, 4) in y = -5/2 x + c, we get,

(-5/2) (-2) + c = 4

c = -1

So the equation is, y = -5/2 x - 1

Hence the required equation is y = -5/2 x - 1.

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Answer:

[tex]y-x = 16[/tex]

Step-by-step explanation:

Given

Set 1: (9,5,y,2,x)

Set 2: (8,x,4,1,3)

Required

(y - x)

First the mean values of set 1 and set 2 has to be calculated

For set 1

[tex]Mean _1 = \frac{(9+5+y+2+x)}{5}[/tex]

Collect like terms

[tex]Mean _1 = \frac{9+5+2+y+x}{5}[/tex]

[tex]Mean _1 = \frac{16+ y+x}{5}[/tex]

For set 2

[tex]Mean _2 = \frac{(8+x+4+1+3)}{5}[/tex]

Collect like terms

[tex]Mean _2 = \frac{8+4+1+3+x}{5}[/tex]

[tex]Mean _2= \frac{16+ x}{5}[/tex]

Given that the mean of set 1 is twice the mean of set 2;

[tex]Mean_1 = 2Mean_2[/tex]

[tex]\frac{16+ y+x}{5} =2 * \frac{16+x}{5}[/tex]

Multiply both sided by 5

[tex]5 * \frac{16+ y+x}{5} = 5 * 2 * \frac{16+x}{5}[/tex]

[tex]16+ y+x = 2 * (16+x)[/tex]

Open bracket

[tex]16+ y+x = 32 + 2x[/tex]

Subtract 16 from both sides

[tex]16+ y+x- 16 = 32 + 2x - 16[/tex]

[tex]16 - 16 + y+x = 32 - 16 + 2x[/tex]

[tex]y+x = 16 + 2x[/tex]

Subtract 2x from both sides

[tex]y+x-2x = 16 + 2x-2x[/tex]

[tex]y-x = 16[/tex]

Answer:

B. 4x² - 20x  + 26

Step-by-step explanation:

→Set it up, like so:

(2x - 5)² + 1

4x² - 20x + 25 + 1

→Add like terms (25 and 1):

4x² - 20x + 26

Answer:

385 ways

Step-by-step explanation:

Given;

7 red balls

10 white balls

In how many ways can 4 balls be selected if there are more than 2 red balls.

Selecting 4 balls which must contain more than 2 red balls, will be 3 red balls and 1 white ball to make it 4 in total, or all the 4 balls selected will red balls.

= 3 red balls and 1 white ball  OR 4 red balls

= 7C₃ x 10C₁  + 7C₄

[tex]= \frac{7!}{4!3!} *\frac{10!}{9!1!} \ \ + \ \frac{7!}{3!4!} \\\\= (35*10) \ + \ 35\\\\= 350 \ + 35\\\\= 385 \ ways[/tex]

Therefore, there are 385 ways of selecting 4 balls, if there are more than 2 red balls.

Answer:

230,000

Step-by-step explanation:

You have round in the ten thousands space which is the 3, knowing that the next number is 8 and it is greater than 5 the 3 will round up to a 4

Answer:

a) The probability that fewer than five of them have type o negative blood is 0.1275

b) The probability that fewer than five of them have type o negative blood is 0.9933

c) 0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have type o negative blood, or they do not. The probability of a person having type o negative blood is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

7% of U.S. residents have type o negative blood.

This means that [tex]p = 0.07[/tex]

18 donors.

This means that [tex]n = 18[/tex]

(a) What is the probability that three or more of them have type o negative blood?

Either less than three have, or at least three do. The sum of the probabilities of these events is 1. So

[tex]P(X < 3) + P(X \geq 3) = 1[/tex]

We want [tex]P(X \geq 3)[/tex]

So

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]

[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]

[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2708 + 0.3669 + 0.2348 = 0.8725[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.8725 = 0.1275[/tex]

The probability that fewer than five of them have type o negative blood is 0.1275

(b) What is the probability that fewer than five of them have type o negative blood?

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]

[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]

[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]

[tex]P(X = 3) = C_{18,3}.(0.07)^{3}.(0.93)^{15} = 0.0942[/tex]

[tex]P(X = 4) = C_{18,4}.(0.07)^{4}.(0.93)^{14} = 0.0266[/tex]

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.2708 + 0.3669 + 0.2348 + 0.0942 + 0.0266 = 0.9933[/tex]

The probability that fewer than five of them have type o negative blood is 0.9933.

c) Would it be unusual f none of the donors had type o negative blood?

[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]

0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.

Answer:

There is a probability of 86.6% that the sample mean falls within 0.03 percent of the raw purity mean.

Step-by-step explanation:

We have a population standard deviation of σ ≈ 0.1.

We have a sample of size n=25.

Then, we have a sampling distribution, which has a standard deviation for the sample mean that is:

[tex]\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.1}{\sqrt{25}}=\dfrac{0.1}{5}=0.02[/tex]

Now, we can calculate a z-score for a deviation of 0.03 percent from the mean as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{0.03}{0.02}=\dfrac{0.03}{0.02}=1.5[/tex]

Note: we considered that the margin is ±0.03.

Then, the probability is:

[tex]P(|X-\mu|<0.03\%)=P(|z|<1.5)=0.866[/tex]

Answer:

P(odd number) = 0.5

Step-by-step explanation:

There are 90 members in the set (10, 11, 12, .. , 97, 98, 99)

When we have an even number of consecutive numbers, the number of even numbers equals the number of odd numbers. This means that half of the numbers in this set are even and half of them are odd.

So the probability of P(odd number) = 0.5

Answer:

[tex]y^2+88y+484[/tex]

Step-by-step explanation:

[tex]4(y+11)^2-3y^2= \\\\4(y^2+22y+121)-3y^2= \\\\4y^2-3y^2+88y+484= \\\\y^2+88y+484[/tex]

Hope this helps!

Answer:

The correct option is (A).

Step-by-step explanation:

If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.

[tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]

Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:

[tex]\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right][/tex]

Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.

Thus, the correct option is (A).

Answer: The value is 18.

Step-by-step explanation:

Since we already know what p, q, and r equal, we can use what we know and plug in the numbers:

p=7, q=5, and r=3,

p2=7*2=14

q2=5*2=10

r2=3*2=6

In conclusion, 14+10-6=18

The value of p2+q2-r2 is 18.

Answer:

Just simply change the variables with their values

7 x 2 + 5 x 2 - 3 x 2

14 + 10 - 6

24 - 6 = 18

18 is the answer

Hope this helps

Step-by-step explanation:

Answer:  nice and funnyyyyy y=4

Step-by-step explanation:

Answer:

360 x 30% = answer

30% = 30/100 = 0.3

360 x 0.3 = 108

108 is the answer

Hope this helps

Step-by-step explanation:

Answer:

108 pages

Step-by-step explanation:

30% of 360=108

360*.30=108

Answer:

m=2

Step-by-step explanation:

-2.73m-10.92=-6m-4.38

3.27m=6.54

m=2

Answer:

Step-by-step explanation:

Hello!

The sample shows the scores for the combined three-part SAT.

Raw data in first attachment.

a.

To arrange the data in a frequency table using class intervals you have to determine the number of intervals you want to use and calculate their width. In this case, the width is given and so is the lower limit of the first interval, you calculate the successive limits by adding the width. The lower limit of the next interval will be the upper limit of the previous one:

1) 800 + 200= 100

First interval [800; 1000)

2) 1000 + 200

Second interval

[1000; 1200)

And so on until you reach the maximum value of the data set,

[1200; 1400)

[1400; 1600)

[1600; 1800)

[1800; 2000)

[2000; 2200)

Then you have to order the data from least to greatest and count how many observations correspond to each value, this way you'll determine the observed frequency for each interval.

Table and histogram in second attachment.

b.

As you can see in the histogram, this distribution is symmetrical centered in the interval [1400; 1600) and there are no outliers observed.

c.

Values around 1400-1600 are the most common ones while scores around 800-1000 or 2000-2200 are more uncommon, in this sample it seems the probability to obtain a perfect score for the combined three-part SAT is extremely low.

I hope you have a nice day!

Answer:

Step-by-step explanation:

Given that:

A small-business Web site contains 100 pages and 60%, 30%, and 10%  of the pages contain low, moderate, and high graphic content, respectively.

. A sample of four pages is selected without replacement,

Let  X and Y denote the number of pages with moderate and high graphics output in the sample

We are meant to determine

a)  [tex]f_{XY}(x, y)[/tex]  from the given data in the question;

However; the probability mass function can be expressed via the relation:

[tex]f_{XY}(x,y) = \dfrac{(^{30} _x ) ( ^{10} _y ) (^{60} _ {4-x-y} ) }{ ( ^{100}_4)}[/tex]

We can now have a table shown as :

[tex]X|Y[/tex]                0           1               2              3              4          Total    [tex]f_X(x)[/tex]

0              0.1244     0.0873     0.02031    0.0018     0.0001   0.234

1               0.2618     0.13542   0.02066    0.00092    0         0.419

2              0.1964     0.0666    0.00499       0              0         0.268

3              0.0621     0.01035     0                 0              0         0.073

4              0.0069       0              0                0              0          0.007

Total [tex]F_Y(y)[/tex]   0.6516   0.2996   0.0460      0.0028  0.0001    1

b) [tex]f_X(x)[/tex]

The marginal distribution definition of [tex]f_X(x)[/tex][tex]= P(X=x)[/tex]

[tex]f_X(x)[/tex] [tex]= \sum P(X=x, Y=y)[/tex]

From the table above ; the corresponding values of [tex]f_X(x)[/tex]  are :

X           0           1         2          3           4

[tex]f_X(x)[/tex]    0.234   0.419  0.268   0.073    0.007

( since [tex]f_X(x)[/tex] represent the vertical column)

c) E(X)

By using the expression [tex]E(x) = \sum ^4 _{x= 0} x f_X(x)[/tex]

we have:

E(X) = [tex]0*0.234+1*0.419+ 2*0.268+3*0.073+4*0.007[/tex]

E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028

E(X) = 1.202

d) fyß(y)

Using the thesis of conditional Probability; we have :

[tex]P(A|B) = \dfrac{ P(A,B) }{ P(B) }[/tex]

The conditional probability for the mass function is then:

[tex]f_{Y|X=3}(y) = \dfrac{f_{XY}(3,y)}{f_{X}(x)}[/tex]

where;

[tex]f_X(3) = 0.0725[/tex]

values of [tex]f_{XY} (3,y)[/tex] for every y ∈ (0,1,2,3,4)

Therefore; the mass function is:

[tex]Y|{_X_3}:\left[\begin{array}{ccccc}0&1&2&3&4\\0.857&0.143&0&0&0\\ \end{array}\right][/tex]

e) E(Y | X = 3)

By using the expression [tex]E(Y|X=3) = \sum ^4 _{y= 0} y f_{y \beta} \ (y|x)[/tex]

we have:

⇒ [tex]0 * 0.857 + 1*0.143 +0 +0+0[/tex]

= 0.143

The value of E(Y | X = 3) = 0.143

g) Are X and Y independent?

To Check if X and Y independent; Let assume if [tex]f_{XY}(x,y) = f_X(x)f_{Y}(y)[/tex] ; then we can say that X and Y are independent.

From the above previous table :

[tex]f_{(XY)} (0.4) = 0.0001[/tex]

[tex]f_X (0)[/tex] = 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001

[tex]f_X (0)[/tex]  = 0.234

[tex]f_X (4)=0.0001 +0+0 \\ \\ = 0.001[/tex]

[tex]f_{X}(0) f_Y(4) = 0.234*0.0001[/tex]

[tex]f_{X}(0) f_Y(4) = 0.00002[/tex]

We conclude that [tex]f_{(XY)} (0.4) \neq f_X(0) f_Y(y)[/tex]; As such X and Y are said to be  non - independent.

Answer:

see below

Step-by-step explanation:

i is the imaginary number and it represents the square root of -1