1. (20 points) Point Estimator Assuming X is a Bernoulli random variable. To estimate the parameters of X, we perform n

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1 20 Points Point Estimator Assuming X Is A Bernoulli Random Variable To Estimate The Parameters Of X We Perform N 1 (182.07 KiB) Viewed 19 times

1. (20 points) Point Estimator Assuming X is a Bernoulli random variable. To estimate the parameters of X, we perform n iid trials and count the number of successes k. k n Suppose we obtain the estimate the success probability (p) of X by ô = a) (10 pts) Is Ộ an unbiased estimator for p? What is the mean square estimation error of p? Hint: k is a binomial(n,p) random variable. If we obtain the estimate of the variance (02) of X by k k 1 - 4 / ô 2 n b) (5 pts) Show that ô 2 is a biased estimator for the variance of X. c) (5 pts) Find a factor c, such that cô2 is an unbiased estimator for o2. a