Let y 1 , y 2 , , y n be a random sample from a gamma distribution with parameters 2 and unknown a Show that y is a biased estimator of Compute the bias b Show that y 2 is an unbiased estimator of c Find the variance of y 2 Recall that, for a gamma distribution, E(y i ) 2 and V(y i ) 2 2 ...

a Since the gamma distribution has parameters 2 and the me ...

Let y 1 , y 2 , . . . , y n be a random sample

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Let y₁, y₂, . . . , y_n 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(y_i) = 2β and V(y_i) = 2β².

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Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

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Question Posted: Apr 15, 2021 08:03 AM

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