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.

HINT: If $X \sim \mathrm{Gamma}(\nu/2, 2)$, then $X$ is identical to $\chi^2(\nu)$, the chi-squared distribution with $ν$ degrees of freedom. Conversely, if $Y \sim \chi^2(\nu)$ and $k$ is a positive constant, then $kY \sim \Gamma(\nu/2, 2k)$.
