Question: Let y 1 , y 2 , . . . , y n be a random sample from a gamma distribution with parameters =

Let y1, y2, . . . , yn be a random sample from a gamma distribution with parameters α = 2 and β unknown.

a. Show that y̅ is a biased estimator of β. Compute the bias.

b. Show that β̂ = y̅/2 is an unbiased estimator of β.

c. Find the variance of β̂ = y̅/2. Recall that, for a gamma distribution, E(yi) = 2β and V(yi) = 2β2.

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