Method of moments estimator

Question

Let y1, . . . , yn be a random sample of n observations from a random variable Y with f(y) a gamma density with

α = 2 and unknown β:

f(y) =

( (ye^(−y/β))/β^2 for y > 0

0 else

(a) Find the moment estimator of β

(b) Find E(β hat) and Var(β hat)

Answer 1

Sample Mean (x̄) = E(Y) Sample Variance (s^2) = Var(Y)

Once you have x̄ and s^2 from your observed data, you can solve for parameter β.