Let $\mathrm{X}$ and $\mathrm{Y}$ be independent exponential random variables with common parameter $\lambda$. If $z=\mathrm{X}+3 \mathrm{Y} $ and $W=3 \mathrm{X}+\mathrm{Y}$, find the joint pdf of $(z, W)$. Lutfen birini secin: a. $f_{Z W) (z, w:- \frac{\lambda {2}}{8} ^{- \frac{\lambda (z+w) }{4}}$ b. $f_{Z W}(z, w)=\frac{\lambda^{2}}{8} e^{- \frac{\lambda (x+w) }{4}}$ c. $f_{Z W) (z, w)=\frac{\lambda^{2}}{8} e^{- \{}{ \lambda (z+w)>$ d. $f_{2 W}(z, w)=8 \lambda [2] e^{-\frac{\lambda (z+w)}{4}}$ ef $f_{Z W) (z, w)=\frac{\lambda^{2}}{8} e{- \frac{\lambda (x+2 w)}{4}}$ SP.SD.009