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Word Problem - Expected Value

  1. Feb 28, 2013 #1
    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...

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

    But if i evaluate this i'm going to get either 0 or infinity... So should this just be an indefinite integral?
  2. jcsd
  3. Feb 28, 2013 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    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
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