# Question: Derive the formulas for the mean and the variance of

Derive the formulas for the mean and the variance of the Poisson distribution by first evaluating E(X) and E[ X(X – 1)].

## Answer to relevant Questions

Show that if the limiting conditions n → ∞, θ → 0, while n. remains constant, are applied to the moment–generating function of the binomial distribution, we get the moment-generating function of the Poisson ...Use the result of Exercise 5.3 to show that for the Bernoulli distribution, (a) α3 = 1 – 2θ / √(1 - θ), where α3 is the measure of skewness defined in Exercise 4.26 on page 129; (b) α4 = 1 – 3θ(1 - θ) / √(1 - ...With reference to Exercise 5.44, suppose that the percentage had been 51 instead of 50. Use a suitable table or a computer printout of the binomial distribution with n = 18 and θ = 0.51 to rework the three parts of that ...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 ...Find the mean and the variance of the hypergeometric distribution with n = 3, N = 16, and M = 10, using (a) The results of Exercise 5.64; (b) The formulas of Theorem 5.7.Post your question