Suppose that X1,....,Xn form a random sample from a normal distribution for which both the meanmand variances^2 are unknown.

Let the random variable L denote the length of the shortest confidence interval formthat can be constructed from the observed values in the sample.

Find the value of E(L^2) for the following values of the sample sizenand the confidence coefficienty:

a.n= 5,y= 0.95 (Ans: 6.16 s^2)

b.n= 8, y = 0.90 (Ans:2.05 s^2)