1. Let X denote the mean of a random sample of size 75 from the distribution that has the pdf f (x) =1, 0<=x<=1. Calculate P (0.45 <X< 0.55). 2. Derive the moment-generating function for the normal density. 3. Let Y n (or Y for simplicity) be b (n, p). Thus, Y / n is approximately N [p, p (1 -p) / n]. Statisticians often look for functions of statistics whose variances do not depend upon the parameter. Can you find a function, say u(Y / n), whose variance is essentially free of p? can anyone help me with them?