Sums and Linear combinations of normal random variables are also normally distuributed. Suppose W, X and Y are independent normal random variables.
W N (0,3) ? = 0 ? = 3
X N (3,4) ?=3 ? = 4
Y N (5,2) ?= 5 ? = 2
a) Find the variance of 5Y +4X -2W
b) Find the expected value of 5Y +4W - 2W
c) Find the standard devation of 5Y + 4X - 2W
d) Find the probability P (5Y +4X - 2W > 30)
e) What is the covariance between 3X and 7Y ?