424lab2spring2015

# 424lab2spring2015 - Eric Zivot Econ 424 Spring 2015 Problem...

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Eric Zivot Econ 424 Spring 2015 Problem Set #2 Working with Random Variables and Probability Distributions Due: Tuesday 4/14/15 at 8pm via Canvas 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) and Appendix (probability review) 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 Hint : you can use the R functions pnorm() and qnorm() to answer these questions. 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.

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• Fall '08
• Yu,W
• Normal Distribution, continuously compounded return, monthly return, rt rt, simple monthly return

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