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stat420_hw1 - STAT 420 Homework 1 Spring 2014 Due February...

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STAT 420 Spring 2014 Homework 1: Due February 4 by 7:00pm Exercise 1 (a) At Anytown College, the heights of female students are normally distributed with mean 66 inches and standard deviation 1.5 inches. The heights of male students are also normally distributed with mean 69 inches and standard deviation 2 inches. For Homecoming, a male student and a female student are selected independently at ran- dom to be the King and the Queen. What is the probability that the female student selected to be the Queen is taller than the male student selected to be the King? (b) Suppose that a population of married couples in Anytown have heights in inches, X for the wife, and Y for the husband. Suppose that ( X, Y ) has a bivariate normal distribution with parameters μ X = 66 , σ X = 1 . 5 , μ Y = 69 , σ Y = 2 , ρ = 0 . 44 . What is the probability that the wife is taller than her husband? Exercise 2 Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y
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