The problem is very straightforward and it says:
Let $X_1,X_2,X_3$ independent random variables with a common density $f_{x_i} \sim Uniform(1,2)$. Define $Y = X_1 X_2 / X_3$ Find the numeric value of $var(Y)$.
I propose the following transformation in order to compute the density of $Y_1$ through the margin distribution, and then compute the variance of $Y_1$:
$$ Y_1 = X_1 X_2 / X_3 $$ $$ Y_2 = X_2/X_3 $$ $$ Y_3 = X_3 $$
But I'm not getting any results. Is there an easy path to follow?
Disclaimer: I tried to solve the problem with this technique because I wanted to practice the topic of transformation of random variables.
self-study
tag and read its wiki. $\endgroup$