1.20 marks Let , be i.i.d. samples of a random variable X with mean and variance . Consider the following estimators of : i=1 2x1-x5+3 2= 2 (a) Is either estimator unbiased? (b) Which of these two estimators is better? In what sense is it better?
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In this case, we want to check if the expected value of each estimator is equal to the true mean . For the first estimator, we have: E[1] = E[2X1 - X5 + 3] = 2E[X1] - E[X5] + 3 Since the samples are i.i.d., we can assume that E[X1] = E[X2] = ... = E[X5] = . Show more…
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