1. Within one hour, the number of orders at a take-away restaurant is a Poisson random variable N with mean /= 15. The amounts in dollar spent by different customers are i.i.d. random variables X1, X2,….. with a uniform distribution on [6,12]. (i) Find the expression of the total amount X, as a random variable, received by the restaurant, (ii) Find EX.2. Suppose X and Y are independent and each have a uniform distribution on the interval (0,1). Use conditioning to find P{X < (0.5)Y}.