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

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Basic Math

A poker hand (5 cards) is dealt off the top of a well-shuffleddeck of 52 cards. Let X be the number of diamonds in the hand. LetY 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 ithcard 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 ithcard is a heart and 0 otherwise. Of course, E[Hi] is the same asE[Di], since there are the same number of hearts as diamonds in a52-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 ofcovariance, of course) to calculate Cov[X,Y].

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