- #1

TheMathNoob

- 189

- 4

## Homework Statement

Supposethat X1and X2 are .random variables and that each of them has the uniform distribution on the interval [0, 1]. Find the p.d.f. of Y =X1+X2.

## Homework Equations

Find cdf of Y and then the pdf

## The Attempt at a Solution

the joint pdf would be f(x1,x2)= 1 0<x1<1 0<x2<1

0 otherwise

so I have to compute the prob that pr(Y<y)= pr(x1+x2<y). If we graph y=x1+x2 over the x2 , x1 axes, then we can say that x2=y-x1 and y would be like the shifting value of the line. The defined region is a square and the region of integration would the area defined by this line and the square. I don't understand how to set the boundaries and the integrals. They are confusing me a lot. I would accept an explanation on a scratch paper to see the big picture of it. I would appreciate if you explain how to approach those kind of exercises that involve two random variables using the definition and the logic of pr(x1+x2<y). The manual solution gives two different pdfs.