Let X be a random variable which denotes the number of failures in a sequence of...
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Let X be a random variable which denotes the number of failures in a sequence of independent Bernoulli trials, each with success probability p, before observing the rth success. That is, X follows the negative binomial distribution with success probability p and number of successes r. Prove that r(1– p) E(X)= р Note that the negative binomial distribution described on Wikipedia is defined differently than the one in our course, and thus gives a different expected value. Let X be a random variable which denotes the number of failures in a sequence of independent Bernoulli trials, each with success probability p, before observing the rth success. That is, X follows the negative binomial distribution with success probability p and number of successes r. Prove that r(1– p) E(X)= р Note that the negative binomial distribution described on Wikipedia is defined differently than the one in our course, and thus gives a different expected value.
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Probability and Statistics
ISBN: 978-0321500465
4th edition
Authors: Morris H. DeGroot, Mark J. Schervish
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