1. Suppose X1 is normally distributed with a mean of 3 and a standard deviation of 1 and suppose X2 is normally distributed with a mean of 4 and a standard deviation of 2. (a) For independent samples of sizes 8 and 10, respectively, find the mean and standard deviation of X, - X2. (3 marks) (b) Would your answers in (a) change if X, and/or X2 were not normally distributed? Explain your answer. (2 marks) (c) Explain why X1 - X2 is normally distributed, despite the fact that both n, and nz are small. (2 marks) (d) Suppose two independent samples are randomly obtained from populations 1 and 2, with sample sizes n = 8 and n2 = 10. Compute the probability that either sample average is at least 2 greater than the other. (6 marks)