Expected Value

**laser** · April 21st 2009, 05:52 PM

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.

**mr fantastic** · April 21st 2009, 06:00 PM

Originally Posted by laser

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 ....?

**laser** · April 26th 2009, 06:36 PM

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.

**mr fantastic** · April 26th 2009, 08:13 PM

Originally Posted by laser

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.

**laser** · April 26th 2009, 08:42 PM

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.

**mr fantastic** · April 26th 2009, 08:50 PM

Originally Posted by laser

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.

**laser** · April 26th 2009, 08:53 PM

I got it! That was it. You're the best. Thanks a million!

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