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## Homework Statement

X1 and X2 are independent~u(0,1)

Y1=X1+X2

Y2=X1-X2

Find the density function of Y1

## Homework Equations

X1=(Y1+Y2)/2

X2=(Y1-Y2)/2

0[tex]\leq[/tex]Y1[tex]\leq[/tex]2

-1[tex]\leq[/tex]Y2[tex]\leq[/tex]1

0[tex]\leq[/tex]Y1+Y2[tex]\leq[/tex]2

0[tex]\leq[/tex]Y1-Y2[tex]\leq[/tex]2

-y1[tex]\leq[/tex]y2[tex]\leq[/tex]2-y1

-1[tex]\leq[/tex]y2[tex]\leq[/tex]y1

## The Attempt at a Solution

I don't understand how to set up the upper and lower bounds for these problems. I have spent the last two days wrestling with this, and I just don't get it. My professor spent almost an hour today trying to explain this to me, and I got nothing out of it. I will send a chocolate chip cookie through the mail to whoever can explain this in a way that I will finally understand. And while you're at it, maybe you can tell me if I should have used whomever in the last sentence, because that's another thing beyond my comprehension.