Question 1. You would like to design a sample mean estimator Mn(x) of the expected value of a random variable X with un

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Question 1.
You would like to design a sample mean estimator
Mn(x) of the expected value of a
random variable X with unknown mean and variance 4. You desire a
confidence interval estimate of (Mn(X) −
3c/4, Mn(X) + c/2) with confidence 0.95. Assume c =
0.01. Derive a bound on the number n of samples that
one must observe.
Suppose you are told that X is a sum of 10 independent Gaussian
random variables, each with variance 0.4.
How would you revise your above derived bound?
Suppose you use each of the above estimators separately to come up
with 1000 estimates of the expected value.
On an average, how many of your estimates would you expect to
satisfy the confidence interval? Answer this for
both the estimators.