# Question

A variation of the binomial distribution arises when the n trials are all independent, but the probability of a success on the ith trial is θi, and these probabilities are not all equal. If X is the number of successes obtained under these conditions in n trials, show that

(a) µX = n., where

(b) σ2X = nθ(1 – θ) – nσ2θ , where θ is as defined in part (a) and

(a) µX = n., where

(b) σ2X = nθ(1 – θ) – nσ2θ , where θ is as defined in part (a) and

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