2027Hmwk4

# 2027Hmwk4 - ISyE 2027 R D Foley Probability with...

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ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Homework 4 September 15, 2011 due Wednesday 1. Suppose you’re dealt 6 cards from a standard deck. Let X be the number of hearts in the hand. (a) Compute the p.m.f. of X . Let Y be the number of clubs in the hand. (b) Compute the joint p.m.f. of X and Y . That is, compute P { X = i , Y = j } for all i and j . (Please leave your answer in the form of a nice expression involving terms like ( n k ) .) 2. Suppose P { X = k } = ± ck 2 for k = ± 1, ± 2 , 0 otherwise. (a) What is the correct value of c ? (b) Compute P { X = - 1 } . (c) Compute E [ X ] . (Was that answer surprising?) (d) Compute E [ X 2 ] . (e) Find all medians of X . (f) Is the following true: E [ X 2 ] = E [ X ] 2 ? 3. Let A be an event. Let I A be the indicator random variable of the event A . That is, I A = ± 1 if A occurs, 0 if A does not occur (a) Compute the p.m.f. of I A . (b) Compute E [ I A ] . (c) Compute E [ I 2 A ] . 4. Let

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2027Hmwk4 - ISyE 2027 R D Foley Probability with...

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