Warrenty payout?

At time of purchase, the value of a certain TV is $1000, and its value in the future is given by w(t) = 12.5(3^(4-t) -1) 0<=t<=4, where t is the time in years (after 4 years, the TV has no more value with respect to warranty). If it fails during the first four years, the warranty pays w (t). Compute the expected valueof the payment on the warranty if the lifetime distribution of the TV is exponential with expectation 10 years.(Note: 3^x=e^(x ln 3 ) • October 24th 2009, 05:36 PM mr fantastic Quote: Originally Posted by affelix At time of purchase, the value of a certain TV is$1000, and its value in the future is given by w(t) = 12.5(3^(4-t) -1) 0<=t<=4, where t is the time in years (after 4 years, the TV has no more value with respect to warranty). If it fails during the first four years, the warranty pays w (t). Compute the expected valueof the payment on the warranty if the lifetime distribution of the TV is exponential with expectation 10 years.(Note: 3^x=e^(x ln 3 )
Use the known pdf of the exponential distribution, f(t), to calculate the expected value of W: $E(W) = \int_0^{+\infty} w(t) f(t) \, dt = \int_0^4 w(t) f(t) \, dt$.