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A standard deck of 52 cards is shuffled and dealt. Let X1 be the number of...

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Basic Math

A standard deck of 52 cards is shuffled and dealt. Let X1 be thenumber of cards appearing before the first ace, X2 the number ofcards between the first and second ace (not counting either ace),X3 the number between the second and third ace, X4 the numberbetween the third and forth ace, and X5 the number after the lastace. It can be shown that each of these random variables Xi had thesame distribution, i=1,2,...,5, and you can assume this to betrue.

a) Write down a formula for P(Xi=k), 0≤k≤48

b) Show that E(Xi)= 9.6 (Hint:Don't use your answer to parta)

c) Are X1,X2,...,X5 pairwise independent? Prove your answer.

Answer & Explanation Solved by verified expert
4.4 Ratings (938 Votes)
Let X1 be the number of cards appearing before the first acePX1 0 452 113 since its Pfirst card is AcePX1 1 4852 no ace first 4 51 Ace secondPX1 2 4852 4751 450 no ace no ace    See Answer
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