Show transcribed image text 1. Let Xi, X,..,Xn be a random sample with the common pdf where Î¸ 1. (a) Determine what the sample average X converges to, in probability. (b) what does converge to? Show your work. 2. Suppose X has a binomial distribution with r 100 and p = 0.043. Suppose we want to find P(2 sX S 8). (a) Determine the exact probability, using R. (b) Use the CLT to approximate this probability. Obtain the approximation without the continuity correction and with the continuity correction.

1. Let Xi, X,..,Xn be a random sample with the common pdf where Î¸ 1. (a) Determine what the sample average X converges to, in probability. (b) what does converge to? Show your work. 2. Suppose X has a binomial distribution with r 100 and p = 0.043. Suppose we want to find P(2 sX S 8). (a) Determine the exact probability, using R. (b) Use the CLT to approximate this probability. Obtain the approximation without the continuity correction and with the continuity correction.