Using a Bayesian latent growth curve model to identify by Elliot M. R.

By Elliot M. R.

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Additional info for Using a Bayesian latent growth curve model to identify trajectories of positive affect and negative events following myocardial infarction

Sample text

That is the sort of problem you'll find in this book. And where did these problems come from, you may wonder. During the past twenty-five years, I have taught (and continue to teach) probability theory to undergraduate electrical engineering students at the University of New Hampshire. ) At the end of each term there are always pleas to provide some sort of extra credit work with which to bolster grades, and I have responded by Ifltrodi/6-tioKi 5" offering what I call "Challenge Problems," These are optional problems (students have to accept the challenge before seeing the problem, and after seeing it, they can't change their minds) to be done as "take-homes" during the week before the final exam (independent work only), with unlimited time, and no partial credit.

1. Imagine that each of the n switches is, independently, either closed with probability p or open (as each is shown in the figure) with probability 1 — £>. What is the probability P\(n, p) that the lamp glows? 1 Sheets of Switches in Series 22 The FfoWewS battery, through the bulb, and back to the negative ( — ) terminal of the battery. As a variation on this problem, imagine that the n sheets are connected in parallel, rather than in series. (Parallel means to connect together the negative terminal of the battery and points AI, A2, .

In the course of a season, however, each team plays many different opponents and the probability of winning against each one clearly depends on the relative strengths of the teams. Still, with that said, I'll continue to use a constant value 5^ Th& ftoblews for p, as this problem will be tough enough even with our gross simplification. After playing n games, we would expect our team to have won np games, although of course it might win any number from none to alL For each possible number of games won—call this number k—we can use the doggy math/Bernoulli trials discussion from the introduction to write the probability of winning k games as In a regular baseball season there are 162 games for each team, so we would expect our team to win I62p games by season's end, and we would expect it to have won 8lp games by midseason.

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