4. Let X,Y be independent Normal r.v. with parameters =0 and g2>0. Show that Y/X has the Cauchy density. Hint: Call U=Y/X and V=X, and find joint density first. then marginal.
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Since X and Y are independent, their joint density is the product of their individual densities. Show more…
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If $X$ and $Y$ are independent standard normal random variables, determine the joint density function of $$ U=X \quad V=\frac{X}{Y} $$ Then use your result to show that $X / Y$ has a Cauchy distribution.
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