# Word Problem - Expected Value

1. Feb 28, 2013

### twoski

1. The problem statement, all variables and given/known data

Suppose that if you are s minutes early for an appointment, then you incur cost s * $3, while if you are s minutes late, you incur cost s *$5. Suppose the travel time from your
present location and the location of the appointment is a continuous random variable with
pdf f(x) such that f(x) = (1/10)e-x/10 if x ≥ 0 and f(x) = 0 if x < 0. How many minutes before your appointment should you depart in order to minimize your expected cost?

3. The attempt at a solution

So i want to find E[X] and then the variance i assume...

$E[X] = \int_{0}^{∞} x( 1/10e^{-x/10})$

But if i evaluate this i'm going to get either 0 or infinity... So should this just be an indefinite integral?

2. Feb 28, 2013

### Ray Vickson

Computing EX has nothing to do with the problem. You want to look at expected COST, which will depend on when you leave. Write a formula for the cost function, given that you leave m minutes before your appointment and the trip takes x minutes. Then take the expected value of that cost function.

Last edited: Feb 28, 2013