Let X be a gamma variable with parameters and&nbs

Question

Let X be a gamma variable with parameters $\alpha$ and $\lambda$ , having $E(X) = 6$ and $Var(X) = 3$ . Find $\alpha$ and $\lambda$ . Also, find the m.g.f. of a gamma variable, and hence verify that mean of X is 6 and variance of X is 3 using m.g.f.
b) For married couples living in a certain locality, the probability that the husband will vote in a school board election is 0.21, the probability that they both will vote is 0.15. What is the probability that
i) at least one of them will vote?
ii) neither of them will vote?

09 Jan 2026

Answer :

Word Count : 296

Let X be a gamma variable with parameters α and λ, where λ is the rate parameter. For a gamma distribution, the mean and variance are given by E(X) = α/λ and Var(X) = α/λ². Given E(X) = 6 and Var(X) = 3, we have α/λ = 6 …(1) α/λ² = 3 …(2) Dividing (2) by (1), (α/λ²)/(α/λ) = ______ ___ ______ _________ ________ ______.
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