I am working through several questions for a business statistics (quantitative fin risk) course. Can someone provide me with a detailed way to figure out this question (or a similar one) so that I can better understand it. I missed a large part of the course due to illness. Just catching up now.

3. Log-Returns with same mean and variance, but from different distributions. Con- sider the random variables Y having distribution defined in the previous question and Z, a N(0,1) random variable. These random variables have the same mean and variance. Consider the following model for stock price ST = Spell-2/2)T +ovTW where W is a mean zero, variance 1 random variable. Take So = 50, # = 0.1, o = 0.25, T = 0.5. (a) On the same axis plot the pdfs of Y and Z. Briefly compare. (b) Compute the cdf and pdf of Sy assuming that i. W = Y ii. W = Z Hint: First derive the cdf of Sy in terms of Fw, the cdf of W, and then substitute. On the same axis, plot the pdfs and briefly compare. (c) Derive the quantile function of Sr for each of W = Y and W = Z. Hint: first derive the quantile function in terms of Fw and then substitute. (d) Using the quantile functions compute soos, $0.01, 50.001 where s. is defined as the smallest s such that P(S,