Let y1, y2, y3 be a random sample from a Gamma distribution with alpha = 2 and theta unknown. Is theta= 1/6 y1 + 5/12 y2 − 1/12 y3 an unbiased estimator of theta?
Added by Patrick T.
Step 1
The expected value of theta_hat is E(theta_hat) = E(1/6 y1 + 5/12 y2 - 1/12 y3). Since y1, y2, y3 are random samples from a Gamma distribution with alpha = 2, we know that E(yi) = alpha * theta for i = 1, 2, 3. Therefore, E(theta_hat) = 1/6 * E(y1) + 5/12 * Show more…
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