4. [8 marks] Suppose that X has a "standard half-normal distribution", meaning that its density function is: fx (x) = \\-e 2, 1>0. For parts a) and b), you will need to use Maple syntax to enter your answers. (examples: for 7 write Pi; for _ ze 2 write (1/2)*sqrt(2/Pi)*exp(-*^2/2) ) a) Determine the expected value E(X). E(X) = (click on the preview button to check your answer.) b) Derive fy (y), the density function of Y = 2 + 3X. fy (y) = D, for y E Click for List (click on the preview button to check your answer.) c) You can calculate cumulative probabilities for X from RStudio, using the fact that X = \\Z| (where Z is standard normal) and hence P(X