(Solved): (10 points) Uniform random variables Suppose that, when you buy gas at the gas station, the price ...

(10 points) Uniform random variables Suppose that, when you buy gas at the gas station, the price is uniformly distributed between \( \$ 4.30 \) and \( \$ 4.50 \) per gallon. You plan to buy 12 gallons of gasoline, plus a candy bar for an extra \( \$ 1.00 \). (Assume that there is no tax on your purchase.) (a) (5 points) Find the expected value of the cost of your purchase. (b) (5 points) Find the variance of the cost of your purchase.