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Let $X_1$ and $X_2$ be dependent random variables.

Find the density function for:


Can I use the transformation method to find the conditional density and then use method of conditioning?

$$f(u|x_2)=f_{x_1}(ux_2)\lvert \frac{dx_1}{du}\rvert$$ $$f_U(u)=\int_{-\infty}^\infty f(u|x_2)f(x_2)$$

If not, is there another procedure I can use.


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Impossible to know. What is $f_{x_1}$ (note the small $x_1$)? What is $dx_1/du$? –  Did Sep 11 '13 at 20:37
1) $f_{X_1}$ is the pdf of random variable $X_1$ (it should be a capital, not lowercase). 2) $X_1=UX_2$, therefore $dx_1/du$ is simply $x_2$. –  user90252 Sep 12 '13 at 2:22
You might want to modify your post accordingly. –  Did Sep 12 '13 at 6:05
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