3. (a) Let \( X \) be a random variable having negative binomial distribution with parameters \( k \) and \( \theta \). Find the variance of \( X \). (b) Find the moment-generating function of the Poisson distribution and hence find its mean and variance. (c) If \( \mathrm{X} \) is a random variable having a binomial distribution with the parameters \( \mathrm{n} \) and \( \theta \). then the moment-generating function of
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The variance of a negative binomial distribution is given by the formula \( \text{Var}(X) = \frac{k(1-\theta)}{\theta^2} \). (b) The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring Show more…
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