The daily returns for Twitter stock in 2020 were approximately normally distributed with mean 100p% and standard deviation of a = 4% (Le. the Twitter daily returns were X ~ N(u, 0.0016) written as decimals). For each of the following, be sure to use proper notation and show all steps in your solution (e.g. standardizing X). a. Given that the moment generating function is MX(t) = e0'0008'(2'5+'), find MJ'((t) and use the result to find the mean u. b. Find P(X 3 0.005) and interpret the result. c. Determine the probability that the daily return on Twitter's stock would be at least 2.2% on any given day. d. Suppose that you were looking at the returns on Twitter over many randomly selected days . What proportion of the days should have returns within half a standard deviation from the mean? e. To 4 decimal places, determine the 80th percentile of the distribution and interpret the result