Question

5. (a) Suppose X is a gamma variate with E(x) = 3 and var(X ) = .7 Find the parameters 

α and λ of the gamma distribution. 

Answer 1

A random variable X which has the gamma distribution with a shape parameter $\alpha$ and a rate parameter $\lambda$ (i.e. $X\sim \Gamma (\alpha ,\lambda )$ ) has the following mean and variance:

$E(X)=\alpha/\lambda=3$

$Var(X)=\alpha/\lambda^2=0.7$

Hence

$\alpha=E(X)^2/Var(X)=3^2/0.7=12.857$

$\lambda=E(X)/Var(X)=3/0.7=4.2857$