%20Welch/Downloads/penultimate.pdf CD Page view | A Read aloud Add text | Draw Highligh (un Conditional on p, Is the marcator of A winning the mist game of the maten positively correlated with, uncorrelated with, or negatively correlated with the indicator of A winning the second game? What about if we only condition on the historical data? (e) Given the historical data, what is the expected value for the probability that the match is not yet decided when going into the fifth game (viewing this probability as an r.v. rather than a number, to reflect our uncertainty about it)? . 2. (BH 8.40) An engineer is studying the reliability of a product by performing a sequence of n trials. Reliability is defined as the probability of success. In each trial, the product succeeds with probability p and fails with probability 1 - p. The trials are conditionally independent given p. Here p is unknown' (else the study would be unnecessary!). The engineer takes a Bayesian approach, with p ~ Unif(0, 1) as prior. Let r be a desired reliability level and c be the corresponding confidence level, in the sense that, given the data, the probability is c that the true reliability p is at least r. For example, if r = 0.9, c = 0.95, we can be 95% sure, given the data, that the product is at least 90% reliable. Suppose that it is observed that the product succeeds all n times. Find a simple equation for c as a function of r. 3. (BH 9.1) Fred wants to travel from Blotchville to Blissville, and is deciding between 3 options (involving different routes or different forms of transportation). The jth option would take an average of u, hours, with a standard deviation of o, hours. Fred randomly chooses between the 3 options, with equal probabilities. Let T be how long it takes for him to get from Blotchville to Blissville. (a) Find E(T); Is it simply (# + #2 + #3)/3, the average of the expectations? (b) Find Var(T). Is it simply (of + o? + 03)/3, the average of the variances? -..1.: _1. O S W ALIENWARE