Do The Math Q

An actuary models the lifetime of a device using the random variable Y = 10X^0.8, where X is an exponential random variable with mean 1 year. Determine the probability density function f (y), for y > 0, of the random variable Y.

1. 10y^0.8e^-8y-0.2
2. 8y^-0.2e^-10y0.8
3. 8y^-0.2e^-10y0.8
4. 8y^-0.2e^-(0.1y)1.25
5. (0.1y)^1.25e^{-0.125(0.1y)0.25}
6. 0.125(0.1y)^0.25e^-(0.1y)1.25 Correct Answer

Solution: F

Therefore,