- #1

- 153

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## Homework Statement

f(x,y) = x

^{2}+ xy

^{3}for 0 < x < 1, 0 < y < 2

and 0 otherwise.

Calculate P(X+Y < 1)

## Homework Equations

## The Attempt at a Solution

P(X+Y < 1) = P(X < 1-Y) which means y is now bounded by 0:1 instead of 0:2 and x is bounded by 0:y.

So we get ∫

_{[0-1]}∫

_{[0-y]}x

^{2}+ xy

^{3}dx dy

Integrating twice I get the answer P(X < 1-Y) = 1/8, which is incorrect.

What am I doing wrong?