424lab2SolutionsWinter2016

# 424lab2SolutionsWinter2016 - Eric Zivot Econ 424 Winter...

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Eric Zivot Econ 424 Winter 2016 Problem Set #2 Working with Random Variables and Probability Distributions Suggested Solutions Exercises R code for solutions is in the file econ424lab2solutions.R on the class homework page. 1. Suppose X is a normally distributed random variable with mean 0.05 and variance (0.10) 2 . Compute the following Pr(X > 0.10) Pr(X < -0.10) Pr(-0.05 < X < 0.15) 1% quantile, q .01 5% quantile, q .05 95% quantile q .95 99% quantile, q .99 # X ~ N(0.05, (0.10)^2) > mu.x = 0.05 > sigma.x = 0.10 # Pr(X > 0.10) > 1 - pnorm(0.10, mu.x, sigma.x) [1] 0.3085 # Pr(X < -0.10) > pnorm(-0.10, mu.x, sigma.x) [1] 0.06681 # Pr(-0.05 < X < 0.15) > pnorm(0.15, mu.x, sigma.x) - pnorm(-0.05, mu.x, sigma.x) [1] 0.6827 # q.01, q.05, q.95, q.99 > qnorm(c(0.01,0.05,0.95,0.99), mu.x, sigma.x) [1] -0.1826 -0.1145 0.2145 0.2826 2. Let X denote the monthly return on Microsoft Stock and let Y denote the monthly return on Starbucks stock. Assume that X ~ N(0.05, (0.10) 2 ) and Y ~ N(0.025, (0.05) 2 ). Using a grid of values between –0.25 and 0.35, plot the normal curves for X and Y. Make sure that both normal curves are on the same plot. Comment on the risk-return tradeoffs for the two stocks.

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