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

Find the density function for:

$$U=X_1/X_2$$

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.

Thanks!

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  • $\begingroup$ Impossible to know. What is $f_{x_1}$ (note the small $x_1$)? What is $dx_1/du$? $\endgroup$ – Did Sep 11 '13 at 20:37
  • $\begingroup$ 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 $x_2$. $\endgroup$ – Nat Sep 12 '13 at 2:22
  • $\begingroup$ You might want to modify your post accordingly. $\endgroup$ – Did Sep 12 '13 at 6:05

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