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Math Help - Expected Value

  1. #1
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    Expected Value

    The initial value of an appliance is $700 and its value in the future is given by v(t)=100(2^{3-t}-1), 0\let\le3, where t is time in years. Thus after the first 3 years the appliance is worth nothing as far as the warranty is concerned. If it fails in the first 3 years, the warrantee pays v(t). Compute the expected value of the payment on the warranty if T has an exponential distribution with mean 5.
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    Quote Originally Posted by laser View Post
    The initial value of an appliance is $700 and its value in the future is given by v(t)=100(2^{3-t}-1), 0\let\le3, where t is time in years. Thus after the first 3 years the appliance is worth nothing as far as the warranty is concerned. If it fails in the first 3 years, the warrantee pays v(t). Compute the expected value of the payment on the warranty if T has an exponential distribution with mean 5.
    It looks to me like E(payment on the warranty) = \int_0^3 v(t) f(t) \, dt where f(t) is the pdf of T. I assume an answer correct to the nearest cent is all that's required ....?
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    It would be \int (1/5e^{-t/5})(100(2^{3-t}-1). I get an answer of 0.45 using maple but I can't integrate the problem correctly. Hopefully I'm going for the right answer and didn't enter incorrectly into maple. Any ideas? Thank you.
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    Quote Originally Posted by laser View Post
    It would be \int (1/5e^{-t/5})(100(2^{3-t}-1). I get an answer of 0.45 using maple but I can't integrate the problem correctly. Hopefully I'm going for the right answer and didn't enter incorrectly into maple. Any ideas? Thank you.
    Using my TI-89 I get 121.73 (correct to the nearest cent). I doubt you would be expected to get an answer by doing the integration by hand.
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    I keep getting the same answer when integrating using the limits of 0 and 3. I'm sure your answer is the right one. I just can't figure where I am going wrong.
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    Quote Originally Posted by laser View Post
    I keep getting the same answer when integrating using the limits of 0 and 3. I'm sure your answer is the right one. I just can't figure where I am going wrong.
    You are most likely making an input error. Check your brackets etc.
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  7. #7
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    I got it! That was it. You're the best. Thanks a million!
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