Chapter 4.11, Problem 158E

Consider the nail-firing device of Example 4.15. When the device works, the nail is fired with velocity, V, with density

$f(v)=\frac{v^3{e}^{-v/500}}{{\left(500\right)}^4\Gamma \left(4\right)}.$

The device misfires 2% of the time it is used, resulting in a velocity of 0. Find the expected kinetic energy associated with a nail of mass m. Recall that the kinetic energy, k, of a mass m moving at velocity v is k = (mv²)/2.