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HW9 - parameter p Given X = x the conditional probability...

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ECE 302, Homework #9, due date: 3/23/2011 http://cobweb.ecn.purdue.edu/ chihw/11ECE302S/11ECE302S.html Question 1: [Basic] Problem 5.1. (Hint: The most difficult part of this question is how the question is described. Basically, Carlos and Michael each flips a coin twice and there are totally four outcomes. Focusing on the first two outcomes, Carlos computes the number of heads and denotes it by W 1 . Focusing on the last two outcomes, Michael computes the number of heads and denotes it by W 2 . Then X = max( W 1 , W 2 ) and Y = min( W 1 , W 2 ).) Question 2: [Basic] Problem 5.3 Question 3: [Basic] Problem 5.8(a,c,d). Question 4: [Basic] Problem 5.8(f,h,i). Question 5: [Basic] Problem 5.9(b) Question 6: [Intermediate/Exam Level] Problem 5.11. Question 7: [Intermediate/Exam Level] Problem 5.12. In (a), please change the statement to “write down the original sample space S Θ and the new sample space S XY . Question 8: [Intermediate/Exam Level] Suppose X is a geometric random variable with

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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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