The initial value of an appliance is $700 and its dollar value in the future is given by

where t is time in years. Thus, after the first three years, the appliance is worth nothing as far as the warranty is concerned. If it fails in the first three years, the warranty pays v(t). Compute the expected value of the payment on the warranty if T has an exponential distribution with mean 5.

Answer:

Step 1 of 1 :

Given that,

The initial value of an appliance is $7,000 and it's the value in future is

Where t is time in years and has an exponential distribution with mean 5.

Our goal is to find

The expected value of the payment on the warranty if T has an exponential distribution with mean 5.

Now we have find the expected value of the payment on the warranty.

Therefore its p.d.f is

Therefore expected value of payment on the warranty

Therefore the expected value of the payment on the warranty is 121.734.

Conclusion :

If T has an exponential distribution with mean 5.

The expected value of the payment on the warranty is 121.734