Product lifetime is Y=5X^0.7 and X has exponential distribution of . Find distribution function and p.d.f. of Y.

My Guess Work:

So far, I know and since the mean is 1.

When I take the derivative of the equation after substituting for x, I get .

Then multiplying the absolute value of this equation by the original equation of , I get

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