Assume X is distributed student-t with 60 degrees of freedom. You decide to sample 30 observations from X and get a sample mean of 0.5 and sample variance of 1.1. a) Solve for the mean and standard error of the sampling distribution. b) Solve for the probablility of drawing a sample mean at least as extreme as the one you have drawn. c) If you were to increase the sample size to 122, holding all else constant, what would this do to the sample distribution and sampling distribution? (Can explain in words) d) If you were to increase the degree of freedom in the underlying X distribution to 122, holding all else constant, what would this do to the sample distribution and sampling distribution? (Can explain in words)