Homework 7ECO 6416: APPLIED BUSINESS RESEARCH TOOLSFall 2016Submission due date: 12/1/20161. Let Y b

Homework 7ECO 6416: APPLIED BUSINESS RESEARCH TOOLSFall 2016Submission due date: 12/1/20161. Let Y be a random variable. Write the expression for E(Y) and the variance of Y i.e. Var(Y)2. Suppose you assign the following subjective probabilities for your final grade in your statisticscourse (the standard GPA scale of 4 = A to 0 = F applies):GPAProbabilityA=40.20B =30.50C=20.20D=10.08F=00.02a. Calculate your expected GPA in the course?b. Calculate the simple average GPA.c. Is the expected GPA equal to average GPA? Why?d. Calculate the standard deviation of your GPA (eq. 17.2, page 545-546 in the book).e. Standardize GPA i.e. construct standardized variable Z (use eq. 17.3 in the book). 1