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2007 Exam4.1Solutions

# 2007 Exam4.1Solutions - IE 111 9:00 Section Exam 4 Fall...

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IE 111 NAME __________________________ 9:00 Section Exam 4 Fall 2007 Instructions Open book, open notes Clearly indicate your answer You must show all relevant work and justify your answers appropriately Partial credit will be given, but not without sufficient support Each question is worth 33.3 points You do not need to interpolate in tables. Just pick closest value. 40's 2 mean 76.2 50's 355 StDev 13.5 60's 489 N 27 70's 0466788889 Med 77 80's 336789 90's 002 100's 0

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Question 1 Consider the (tri-variate or “three variable”) joint distribution of random variables X, Y, and Z given below. Z=0 Z=1 X=0 X=1 X=0 X=1 Y=0 0 0.3 Y=0 0.1 0 Y=1 0.2 0 Y=1 0 0.15 Y=3 0 0.1 Y=3 0.15 0 a) What is the marginal distribution of X? P(X=0) = 0+0.2+0+0.1+0+0.15 = 0.45 P(X=1) = 0.3+0+0.1+0+0.15+0 = 0.55 b) Find the (bi-variate or “two variable”) joint distribution between X and Z Just sum over Y: X=0 X=1 Z=0 0.2 0.4 Z=1 0.25 0.15 c) Find E(X|Y=0) The conditional joint distribution of X and Z given Y=0, P(x,y|z) is
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2007 Exam4.1Solutions - IE 111 9:00 Section Exam 4 Fall...

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