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hmwk7 - ISyE 2027 R D Foley Probability with Applications...

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ISyE 2027 Probability with Applications Fall 2006 R. D. Foley Homework 7 October 25, 2006 due on Tuesday Please explain your answer to “yes” or “no” questions such as “are X and Y independent”. 1. (30 points) Leave your answer to in terms of ( n k ) . Suppose we are dealt 5 cards from a well-shuffled standard poker deck. Let X be the number of clubs and Y the number of diamonds in the hand. (a) What is the joint probability mass function of X and Y ? (b) What is the marginal probability mass function of Y (c) What is the conditional probability that X = 0 given Y = 4? 2. Roll a pair of dice where each die has 4 sides labelled with the numbers 1, . . . , 4. Let X be the maximum number rolled, and Y be the minimum of the rolled numbers. (a) What is the joint p.m.f. of X and Y ? (b) What is the marginal p.m.f. of X ? (c) What is the conditional p.m.f. of Y given X = 2? (d) What is the E[ Y | X = 2]? 3. Suppose ( X, Y ) has joint p.m.f. Pr { X = i, Y = j } = c (1 + i + j ) for i = 0 , 1 , 2 , j = 0 , 1 , 2 , i + j < 4.
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  • Spring '08
  • Zahrn
  • Probability theory, Probability mass function, marginal probability mass, Poisson random variables, marginal p.m.f., R. D. Foley

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