1. ## Expected Value

The initial value of an appliance is $700 and its value in the future is given by$\displaystyle v(t)=100(2^{3-t}-1)$,$\displaystyle 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. 2. Originally Posted by laser The initial value of an appliance is$700 and its value in the future is given by $\displaystyle v(t)=100(2^{3-t}-1)$, $\displaystyle 0\let\le3$, 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) $\displaystyle = \int_0^3 v(t) f(t) \, dt$ where $\displaystyle f(t)$ is the pdf of T. I assume an answer correct to the nearest cent is all that's required ....?

3. It would be $\displaystyle \int (1/5e^{-t/5})(100(2^{3-t}-1)$. 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.

4. Originally Posted by laser
It would be $\displaystyle \int (1/5e^{-t/5})(100(2^{3-t}-1)$. 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.

5. 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.

6. 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.

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