424lab2SolutionsSummer2014 - Eric Zivot CFRM 462/Econ 424...

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Eric Zivot CFRM 462/Econ 424 Summer 2014 Problem Set #2 Working with Random Variables and Probability Distributions Suggested Solutions Readings My lecture notes on review of probability theory and random variables. A Beginner’s Guide to R, chapters 3-7. R Cookbook, chapters 8 (probability) and 10 (graphics) Ruppert, chapter 2 (Returns). Programs and Data probReview.xls (on class syllabus and homework pages) probReview.r (on class syllabus and homework pages) Instructions In this lab you will become more familiar with random variables and probability distributions. Try to do all of the calculations and plots in R. You can also do everything in Excel too. You will find the examples in probReview.R and probReview.xls to be helpful for some of the exercises that follow. Exercises 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
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