Could anyone tell me what went wrong please. Don`t understand. I have an exercise: $$ f(x)=3x \\ 0 < y < x < 1\\ Find\\ P(X > \frac12 | Y > \frac13) $$ I found that: $$ P(X > \frac12 | Y > \frac13)=\frac{P(X>\frac12\cap Y > \frac13)}{P(Y>\frac13)} $$ which implies to: $$ \frac{\int_\frac12^1\int_\frac13^x3x}{[marginal PDF_y] \int_\frac13^1\frac{3-y^2}{2}} $$ for the upper part I get $$\frac12$$ and for the bottom $$\frac{68}{81} \\ \frac12\div\frac{68}{81}=\frac{81}{136}$$ which is not right answer. Explain please what I did wrong. My teacher insists that I should use the marginal distribution in the denominator.
2026-03-25 23:17:58.1774480678
Why joint distribution exercise goes wrong
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