Then by linearity of expectation, we get the mean of X should be r p ,since the mean of is 1 p. In a hypothetical infinite sequence of trials, let \(U\) denote the number of trials necessary for \(R\) to win \(m + 1\) trials, and \(V\) the number of trials necessary for \(L\) to win \(m + 1\) trials. The negative binomial distribution is more general than the Poisson, and is often suitable for count data when the Poisson is not. The textbook says the mean is r ( 1 p) p, which confuses me because I always consider the negative binomial distribution random variable X as the sum of r independent geometric distributed random variable, P( n) p(1 p)n 1. ![]() Specifically, we can consider a match from the right pocket as a win for player \(R\), and a match from the left pocket as a win for player \(L\).
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