gamma to chi-squared distribution I was checking answers for a question and the following arised:
$$
P(Y>25\mid Y\sim \mathrm{GAM}(15,1)) = P(\chi ^2>3.33\mid\chi^2\sim \chi^2(2)) 
$$
Now i get that chi is just a special case of gamma with $\theta = 2$ and $r=v/2$ but can i just divide everything by $7.5$? It seems like blasphemy.

You have
$$
\Pr(X>x) = e^{-x/15}.
$$
So
$$
\Pr\left(\frac{X}{7.5}>\frac{25}{7.5}\right) = \Pr(X>25) = e^{-25/15} = e^{-(25/7.5)/2}
$$
because
$$
\frac{25}{15} = \frac{2.5/7.5}{2}.
$$
