1. (20 points) Point Emator Asuming X is a Bernoulli random variable to estimate the arms we perform tid trials and coun

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1 20 Points Point Emator Asuming X Is A Bernoulli Random Variable To Estimate The Arms We Perform Tid Trials And Coun 1 (25.03 KiB) Viewed 24 times

1. (20 points) Point Emator Asuming X is a Bernoulli random variable to estimate the arms we perform tid trials and count the number of successes Suppose we obtain the estimate the success probability (p) of Xby a) (10 pts) is p 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 a2 = (1 n b) (5 pts) Show that a 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 ol.