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 a. Calculate E(X). b. Calculate Var(X) c. Let G(X)=8+3X. What is the E[G(X)] and the variance of G(X)?

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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
a. Calculate E(X).
b. Calculate Var(X)
c. Let G(X)=8+3X. What is the E[G(X)] and the variance of G(X)?

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