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2. X has a "standard half-normal distribution", meaning that its density function is: fx () = i) Find E(X). ii) Derive fr(y), the density function of Y = 2+ 3X. iii) You can calculate cumulative probabilities for X using standard normal tables, using the fact that X = [Z| (where Z is standard normal) and hence P(X pnorm ( c(-3, -2, -1, -0.5, 0, 0.5, 1, 2, 3) ) J [1] 0. 0013 0. 0228 0. 1587 0. 3085 0. 5000 0. 6915 0.8413 0.9772 0.9987 qnorm( c(0, 0.125, 0.25, 0. 375, 0.5, 0.625, 0.75, 0.875, 1) ) [1] -Inf -1. 150 -0.674 -0.319 0.000 0.319 0.674 1.150 Inf iv) Find the joint density function of T = x *1 and U = X2 where X, and X2 are independent random variables with density function fx (@) as above