1) [15 points] It is known that the two variables and have variances 5 and 7 res

Question

1) [15 points] It is known that the two variables and have variances 5 and 7 respectively. The covariance between them is known to be .

[5points] a) What is the correlation between the two variables?

[10 points] b) Using the discussion in the slim handout titled “Multivariate distributions and copulas” (there is a similar discussion also to be found around page 90 of the “Multivariate distributions” part of the larger set of course handouts), calculate the variance of the linear combination

You must show all your work in order to get credit. You will get zero points if you just write a number as your answer.

2) [5 points] An analyst is modeling the behavior of two variables. The first variable is adequately described by a normal distribution, but the second variable has thick tails and is adequately described by a t distribution with 5 degrees of freedom. When she studies their joint behavior, she finds that the correlation between the two variables is zero. Would she be correct if she were to therefore assert that the two variables are independent?

a) Yes b) No

Explain your rationale BRIEFLY in a couple of sentences

Explanation / Answer

(2)

Yes the analyst would be correct in asserting that the two variables are not related, because the regression analysis makes the assumption that the residual term ( error term ) is normally distributed. It does not say anywhere that the variables also need to be normally distributed as well.

Hope this helps !

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