iid Consider data X1, X2, ... , Xn Ber(0). Consider the following two estimators of 0 + ;: 1+E, Xi Xn and ô2 2+ n 1. Compute the Bias of both 61 and 02. Which estimator has lower bias (in absolute terms) when 0#= 0? 2. Compute the variance of 01 and 02. Which estimator has lower variance? Hint: com- pute the ratio of Var[0,]/Var[02] and see if the ratio is less than, equal to, or greater than 1.

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Consider data X1, X2, .
X, id
Ber(0). Consider the following
two estimators of 0 + ;:
1+ Σ Χ,
Ô = X, and Ô2
2+n
1. Compute the Bias of both 01 and 02. Which estimator has lower bias (in absolute
terms) when 0 #= 0?
2. Compute the variance of 0, and 02. Which estimator has lower variance? Hint: com-
pute the ratio of Var[01]/Var[02] and see if the ratio is less than, equal to, or greater
than 1.
Transcribed Image Text:Consider data X1, X2, . X, id Ber(0). Consider the following two estimators of 0 + ;: 1+ Σ Χ, Ô = X, and Ô2 2+n 1. Compute the Bias of both 01 and 02. Which estimator has lower bias (in absolute terms) when 0 #= 0? 2. Compute the variance of 0, and 02. Which estimator has lower variance? Hint: com- pute the ratio of Var[01]/Var[02] and see if the ratio is less than, equal to, or greater than 1.
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