# Question: A variation of the binomial distribution arises when the n

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

## Answer to relevant Questions

When calculating all the values of a hypergeometric distribution, the work can often be simplified by first calculating h(0; n, N, M) and then using the recursion formula Verify this formula and use it to calculate the ...Approximate the binomial probability b(3; 100, 0.10) by using (a) The formula for the binomial distribution and logarithms; (b) Table II. Use Theorem 5.9 to find the moment– generating function of Y = X – λ, where X is a random variable having the Poisson distribution with the parameter λ, and use it to verify that σ2Y = λ. With reference to Exercise 5.45 and the computer printout of Figure 5.1, find the probability that among 10 cars stolen in the given city anywhere from 3 to 5 will be recovered, using (a) The values in the P(X = K) column; ...If the probabilities of having a male or female child are both 0.50, find the probabilities that (a) A family’s fourth child is their first son; (b) A family’s seventh child is their second daughter; (c) A family’s ...Post your question