Let X be a Bernoulli Trial population with parameter 0 representing the probability of a success. Let X1,...,X, be a random sample from X and let Y = X (1- X) be an estimator for o = 0(1-0). A. Find a constant c such that cY is an unbiased estimator for o, = 0(1–0). B. Calculate the bias B(Y) C. Interpret this bias in the context of the problem.

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Question 5:
Definition: Let X be a population random variable and let f, (x;0) be the density function for X. Let
O be an estimator for the parameter 0 based on a random sample of observations from X.
1) We define the bias of Ô by B(Ô) = E ô–0|= E
E[ô]-0.
2) If E 0 = 0 then we say 0 is an unbiased estimator of 0, in which case B(0) = 0.
Let X be a Bernoulli Trial population with parameter 0 representing the probability of a success. Let
X1,...,X, be a random sample from X and let Y = X (1-X) be an estimator for o = 0(1-0).
••.
A. Find a constant c such that cY is an unbiased estimator for o, = 0(1-0).
B. Calculate the bias B(Y)
C. Interpret this bias in the context of the problem.
Transcribed Image Text:Question 5: Definition: Let X be a population random variable and let f, (x;0) be the density function for X. Let O be an estimator for the parameter 0 based on a random sample of observations from X. 1) We define the bias of Ô by B(Ô) = E ô–0|= E E[ô]-0. 2) If E 0 = 0 then we say 0 is an unbiased estimator of 0, in which case B(0) = 0. Let X be a Bernoulli Trial population with parameter 0 representing the probability of a success. Let X1,...,X, be a random sample from X and let Y = X (1-X) be an estimator for o = 0(1-0). ••. A. Find a constant c such that cY is an unbiased estimator for o, = 0(1-0). B. Calculate the bias B(Y) C. Interpret this bias in the context of the problem.
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