1) Let X be the hospital period (in days) for patients following treatment for a certain type of kidney
disorder, which is a random variable with probability mass function
f(x) = p (1 - p)x-1 ; x = 1,2; 3....
(a) Find the moment generating function of X;
(b) Find the mean and the variance of X:
2) Let X1;X2; : : : ;Xn be a random sample of size n from a normal distribution N(; 2): Show that
cS is unbiased estimator of , where
c =
r
n