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11ProbHw11

# 11ProbHw11 - IEOR 3658 Probability Prof Mariana...

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IEOR 3658 Assignment #11 Probability November 30, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #11 – due December 12th, 2011 1. Let Y be exponentially distributed with parameter 1, and let Z be uniformly distributed over the interval [0 , 1]. Compute the PDF of W = Y + Z . 2. Find the correlation coefficients for the random variable pairs ( X, Y ) and ( U, V ). X , Y 1 4 7 10 1 0.01 2 0.2 3 0.49 4 0.3 U , V 3 5 7 12 0 0.06 0.12 0.09 0.03 2 0.04 0.08 0.06 0.02 4 0.03 0.06 0.045 0.015 7 0.04 0.08 0.06 0.02 9 0.03 0.06 0.045 0.015 3. Consider n independent tosses of a 6-sided die. Each toss has probability p i of resulting in i . Let X i be the number of tosses that result in i . Show that X 1 and X 2 are negatively correlated (i.e., a large number of ones suggests a small number of twos). 4. Let X and Y be two independent normal random variables with parameters ( μ X , σ 2 X ) and ( μ Y , σ 2 Y ), respectively. Compute the moment generating function of Z = X + Y . What type of distribution does Z have? 5. (From text) Pat and Nat are dating, and all of their dates are scheduled to start at 9 p.m.

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11ProbHw11 - IEOR 3658 Probability Prof Mariana...

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