[7) 5. Short Answers (True-False) For parts are below, we assume S, = X1 + X2+ ...+ X, where the random variables X, are all independent normally distributed random variables with E(X,) = A, Var( X,) = 02. Indicate which of the following are True (T) or False (F). a. S, has a normal distribution with mean ng and variance no' for all n = 1,2, .... T F b. So-" has a standard normal distribution for all n = 1, 2, .... T F F C. On always has a normal distribution and P(|Sa - /| > .(1) - 0 as n - 90. T d, The variance of the sample mean, Var(S" ) - 1 as n - co. T F The correlation coefficient between X1 and S, is p = T F e. f. If X and Y are independent Bin(n, p) random variables T F then X + Y has a Binomial distribution. If X and Y are independent Poisson(#) random variables T F then X + Y has a Poisson distribution