Suppose X is a continuous random variable with a triangular distribution defined over 0 to 2. Picture two right triangles pushed together with a peak at 1. f(x) = 0 for x < 0 f(x) = x for 0 < x < 1 f(x) = 2 - x for 1 < x < 2 f(x) = 0 for x > 2 Calculate E(X). Calculate Var(X) Let G(X)=8+3X. What is the E[G(X)] and the variance of G(X)?.

1. Suppose X is a continuous random variable with a triangular distribution defined over 0 to 2.
Picture two right triangles pushed together with a peak at 1.
f(x) = 0 for x < 0
f(x) = x for 0 < x < 1
f(x) = 2 - x for 1 < x < 2
f(x) = 0 for x > 2
Calculate E(X).
Calculate Var(X)
Let G(X)=8+3X. What is the E[G(X)] and the variance of G(X)?