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A poker hand (5 cards) is dealt off the top of a well-shuffled deck of 52...

A poker hand (5 cards) is dealt off the top of a well-shuffled deck of 52 cards. Let X be the number of diamonds in the hand. Let Y be the number of hearts in the hand.

1. Do you think Cov[X,Y] is positive, negative, or zero? Explain.

2. let Di(i=1,...,5) be a random variable that is 1 if the ith card is a diamond and 0 otherwise. What is E[Di]?

3. let Hi(i=1,...,5) be a random variable that is 1 if the ith card is a heart and 0 otherwise. Of course, E[Hi] is the same as E[Di], since there are the same number of hearts as diamonds in a 52-card deck. What is Cov[Di,Hi]? What is Cov[Di,Hj], when i≠j?

4. Use your answers to parts 2 and 3 (and the properties of covariance, of course) to calculate Cov[X,Y].

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milcah answered 10 months ago
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