Originally Posted by

**jennifer1004** Product lifetime is Y=5X^0.7 and X has exponential distribution of $\displaystyle \lambda=1$. Find distribution function and p.d.f. of Y.

My Guess Work:

So far, I know $\displaystyle x=(y/5)^{10/7}$ and $\displaystyle f(x)=e^{-x}$ since the mean is 1.

When I take the derivative of the equation after substituting $\displaystyle (y/5)^{10/7}$ for x, I get $\displaystyle (-2/35)5^{4/7}y^{3/7}e^{(-1/25)5^{4/7}y^{10/7}}$.

Then multiplying the absolute value of this equation by the original equation of $\displaystyle e^{(y/5)^{(10/7)}}$, I get $\displaystyle (2/25)e^{(-1/25)(5^{4/7}y^{10/7}}5^{4/5}e^{(-1/25)5^{4/7}R(y^{10/7})}|y|^{3/7}$

I really have no idea how to get the right answer to this problem.