Week 13 Preparation Guide

Reading

Required:

• Textbook Chapters 22 and 23

Recommended:

• Skim Section 6.4 of Pitman. We did most of it quite a while ago, but look at the correlation examples 4-6.
• Conditional variance and conditional expectation as a least squares predictor are in Exercises 6.2.17-18, not in the text.
• Pitman’s text doesn’t cover the multivariate normal but it has a good hands-on treatment of the bivariate case in Section 6.5. Much of it is about conditioning, which we’ll do next week. For now, just look at pages 460-461.

Practice Problems

Pitman x.y.z means Exercise z of Section x.y and x.rev.z means Exercise z of the Review Exercises at the end of Chapter x.

• Pitman 4.2.8bc (you did it for homework earlier; now find the expectation and variance by conditioning)
• In Section 21.2 (and in class) we found the expectation of the beta-binomial $(r, s, n)$ distribution by conditioning. Now find the variance.
• On each spin of a Nevada roulette wheel, the winning pocket is red with chance 18/38, black with chance 18/38, and green with chance 2/38. Spins are independent of each other. Given that red pockets won 40 times in the first 100 spins, find:
  • the conditional distribution of the number of times black pockets won
  • the least squares estimate of the number of times black pockets won, and the mean square error of the estimate
• Pitman 6.5.4, 6.5.1, 6.5.8 (are $Y_1$ and $Y_2$ independent?)

Discussion Section

• Nevada roulette wheel, variance of beta-binomial, 6.5.4, 6.5.8