Calculating the joint probability density $e^{-(x+y)}$

Asked Oct 26 '21 at 05:19

Active Oct 26 '21 at 10:10

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I do not understand as to why the joint probability density of $e^{-(x+y)}$ for $x>0, y>0$ when $P(X+Y >3)$, has the following integral bounds $\int_2^3\int_2^3dxdy$

When I sketch the region:

I cannot seem to locate how the lower bounds are 2. How should I interpret regions that involve exponentials?

edited Oct 26 '21 at 09:34

tortue

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asked Oct 26 '21 at 05:19

Stackbeans

1

Those bounds are not correct. – Kavi Rama Murthy Oct 26 '21 at 05:22
@KaviRamaMurthy I believe I might have made a mistake with the pdf. I have updated it – Stackbeans Oct 26 '21 at 05:23
3

I seem to have found someone with the same post: https://math.stackexchange.com/questions/2991252/limits-of-integration-joint-probability-density?rq=1 Turns out to be an error in the book ... – Stackbeans Oct 26 '21 at 05:25
1

Yes definitely an error in the book – Math Lover Oct 26 '21 at 07:39

Calculating the joint probability density $e^{-(x+y)}$

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