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Math 408, Spring 2008 Midterm Exam 2 Solutions

math 408, Spring 2008 Midterm Exam 2 Solutions1. (NO CALCULATORS FOR THIS PROBLEM)(a) Consider the following statements:(1) If Cov(X,Y) = 0, thenXandYare independent.(2) IfXandYare independent, then Cov(X,Y) = one of the following:(i) Only (1) is correct.(ii) Only (2) is correct.(iii) (1) and (2) are both correct.(iv) Neither (1) nor (2) are (ii), , (2) is correct, but not (1). (Note that, while independence implies thatthe covariance is zero, the converse is not true. In fact, a homework problem ( ) gave anexample of two random variables that had 0 covariance, but were not independent.(b) Suppose thatXandYare independent random variables with Var(X) = 1, Var(Y) = Var(1 2X+ 3Y).)

Math 408 Midterm Exam 2 Spring 2008 (b) Find the probability that the amount of the second claim is at least twice that of the first claim. Solution. Let X 1 and X 2 denote, respectively, the first and second claims. Then we need to compute P(X 2 …

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