Consider X and Y two random variables of probability densities p1(x) and p 2(x). respectively. The random variables X and Y are said to be independent if their joint density function is given by p(x,Y) = p1(x)p2(y). At a drive—thru restaurant, customers spend, on average, 3 minutes placing their orders and an additional 5 minutes paying for and picking up their meals. Assume that placing the order and paying for/picking up the meal are two independent events X and Y. If the waiting times are modeled by the exponential
probability densities
respectively, the probability that a customer will spend less than 6 minutes in the drive—thru line is given by
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