The lifetime (in years) equals $\displaystyle Y = 6 X^{0.8}$, where X has an exponential distribution with mean $\displaystyle \frac{1}{2}$.
How do you find the p.d.f. of Y? Tank you for your time.
Just use calc1
$\displaystyle f_Y(y)=f_X(x)\biggl|{dx\over dy}\biggr|$
Where $\displaystyle f_X(x)=2e^{-2x}I(x>0)$
THose ='s should be $\displaystyle \le $ in that scan
That gives you the cdf's and it's derivative gives you the relationship with the densities.