Answer the following questions about joint random variables. (a) When considering the correlation coefficient, does it measure a linear, quadratic, or cubic relationship between the variables? (b) When considering the correlation coefficient, how can you tell if there is a positive relationship, negative relationship, or no relationship between the variables? (c) Suppose we find that the joint probability distribution of X and Y to be x + 2y f(x, y) for x = 0, 1, 2; y= 1,2,3, 4. 72 you were to find the marginal distribution of Y, what would be the sum of the probabilities for the random variable Y be, and why? If

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Answer the following questions about joint random variables.
(a) When considering the correlation coefficient, does it measure a linear, quadratic, or
cubic relationship between the variables?
(b) When considering the correlation coefficient, how can you tell if there is a positive
relationship, negative relationship, or no relationship between the variables?
(c) Suppose we find that the joint probability distribution of X and Y to be
x + 2y
f(x, y)
for x = 0, 1, 2; y = 1, 2, 3, 4.
72
If
you were to find the marginal distribution of Y, what would be the sum of the
probabilities for the random variable Y be, and why?
Transcribed Image Text:Answer the following questions about joint random variables. (a) When considering the correlation coefficient, does it measure a linear, quadratic, or cubic relationship between the variables? (b) When considering the correlation coefficient, how can you tell if there is a positive relationship, negative relationship, or no relationship between the variables? (c) Suppose we find that the joint probability distribution of X and Y to be x + 2y f(x, y) for x = 0, 1, 2; y = 1, 2, 3, 4. 72 If you were to find the marginal distribution of Y, what would be the sum of the probabilities for the random variable Y be, and why?
Expert Solution
Step 1

Given that 

a..When considering the correlation coefficient, does it measure a linear, quadratic, or cubic relationship between the variables...

 

 

b.. When considering the correlation coefficient, how can you tell if there is a positive relationship, negative relationship, or no relationship between the variables....

We have given the joint probability density function of X and Y 

f(x,y)=(x+2y)/72.        for x=0,1,2

                                      for y=1,2,3,4

Then we have to find the marginal distribution of Y and sum of the probabilities of random variable Y is 1...

 

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