m is the probability measure by pdf $\frac{\lambda}{2}e^{-\lambda |r|}$,find the pmf for the random variable $W(r)=3$ if $r\ge 2$ and $W(r)=1$,otherwise .
I know how to find the pdf if the $X(r)=|r|^2$,integral it from $-\sqrt x$ ~ $\sqrt x$,then differentiate it will find the answer,but now the pmf just said $W(r)=3$ if $r\ge 2$ and $W(r)=1$,otherwise,i don't know how to define its summation range
$P\{W(r)=3\}=P\{r\ge 2\}=1-F_R(2)=1-\int_{-\infty}^2 \cfrac {\lambda} {2} e^{-\lambda |t|} \mathrm{d}t=\cfrac 12-\int_0^2 \cfrac {\lambda} {2} e^{-\lambda t} \mathrm{d}t=\cfrac 12 e^{-2\lambda}$
the other pm is just $1-$above.