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 5 and a standard deviation of 2. [a] For independent samples of sizes 8 and 10, respectively, nd the mean and standard deviation of E 1 E. (3 marks) [b] Would your answers in [a] change if X1 and/or X2 were not normally distributed? Explain your answer. (2 marks] [c) Explain why E1 E: is normally distributed, despite the fact that both 111 and 112 are small. (2 marks) Suppose two independent samples are randomly obtained from populations 1 and 2, with sample sizes 111 = 8 and 112 = 10. Compute the probability that either sample average is at least 1 greater than the other. [6 marks)