410Hw05 - STAT 410 Fall 2011 Homework #5 (due Friday,...

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STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distribution with parameters μ X = 370, σ X = 50, μ Y = 270, σ Y = 40, ρ = – 0.80. a) Suppose the government of Neverland spent 450 million dollars on guns during a particular month. Find the probability that more than 250 million was spent on butter during the same month. That is, find P ( Y > 250 | X = 450 ). b) Find the probability that the government of Neverland spends more on guns than on butter during a given month. That is, find P ( X > Y ). c) Find the probability that the government of Neverland exceeds the 700-million spending limit during a given month. That is, find P ( X + Y > 700 ). 2. For a certain population, the blood pressure ( X , Y ) = ( systolic , diastolic ) can be modeled as having a bivariate normal distribution with μ X = 120, σ X = 20, μ Y = 82, σ Y = 15, ρ = 0.6. a) Find the probability that an individual with a diastolic pressure ( Y ) of 91 will have a systolic pressure ( X ) exceeding 140. That is, find P ( X > 140 | Y = 91
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410Hw05 - STAT 410 Fall 2011 Homework #5 (due Friday,...

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