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By Shaked M., Singpurwalla N. D.

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One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin? 43. Suppose we have ten coins which are such that if the ith one is flipped then heads will appear with probability i/10, i = 1, 2, . . , 10. When one of the coins is randomly selected and flipped, it shows heads. What is the conditional probability that it was the fifth coin?

Discrete random variables are often classified according to their probability mass functions. We now consider some of these random variables. 1. The Bernoulli Random Variable Suppose that a trial, or an experiment, whose outcome can be classified as either a “success” or as a “failure” is performed. 2. 2) for some p ∈ (0, 1). 2. The Binomial Random Variable Suppose that n independent trials, each of which results in a “success” with probability p and in a “failure” with probability 1 − p, are to be performed.

13 In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer and 1 − p the probability that she guesses. Assume that a student who guesses at the answer will be correct with probability 1/m, where m is the number of multiple-choice alternatives. What is the conditional probability that a student knew the answer to a question given that she answered it correctly? Solution: Let C and K denote respectively the event that the student answers the question correctly and the event that she actually knows the answer.

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A Bayesian approach for quantile and response probability estimation with applications to reliability by Shaked M., Singpurwalla N. D.


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