Let Y1,...,Yniidf(y) , denote the population mean E(Yi) by , and consider the sample mean as an estimator of (i.e., let Y=^ ). Chebyshev's inequality states that: P |Y^ | > k nk22 In other words, the error of estimation is bounded by k with probability at least 1 nk22 .

(a) Find a sample size n, as a function of 2 , such that 0.01 with probability at least 0.99.

(b) Find the specific values of n that ensure this bound when 2 = 1, 4, 9.

(c) How would you describe the relationship between the population variance and the error of estimation?