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 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)?

2. The table below gives the probability distribution of the number of people per passenger vehicle crossing a toll bridge. a. Calculate E(X). b. Calculate Var(X) c. Operators are considering charging $1 for each car or $0.30 for each passenger. Which choice raises more revenue on average? d. How about the choice between $0.50 for each car versus $0.25 for each passenger? No. People 1 2 3 4 5 6 Probability .05 .43 .27 .12 .09 .04