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Unformatted text preview: parameter p . Given X = x , the conditional probability mass function of Y , p k  X = x = P ( Y = k  X = x ), is a Poisson random variable with α = x . 1. Find the sample space of ( X,Y ). 2. What is the joint probability mass function of X and Y ? 3. What is the marginal probability mass function of X ? 4. What is the probability that P ( X 2 + Y 2 ≤ 4). Question 9: [Basic] Problem 5.25(b,c). Question 10: [Basic] Problem 5.27(a,c,d). Question 11: [Basic] Problem 5.28. Question 12: [Intermediate/Exam Level] Suppose X is a uniform random variable with parameters a = 1 ,b = 2. Given X = x , the conditional probability density function of Y , is an exponential random variable with λ = x . 1. Find the sample space of ( X,Y ). 2. What is the joint probability density function of X and Y ? 3. What is the probability that P ( X < 1 . 5 and Y ≤ 2)?...
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 Spring '08
 GELFAND
 Probability theory, Probability mass function

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