Schaums probability and statistics book gives this problem:
Let X and Y be identically distributed independent random variables with density function:
f(t) = 1 0 \ge t \le 1, 0 otherwise
Find the density function of X + Y. the answer given in the back of the book is
g(u) = u for 0 $\le$ t $\le$ 1, g(u) = 2-u for 1 $\le$ t $\le$ 2 , g(u)=0 otherwise. I cant see why the answer is not just:
g(u) = u for 0 $\le$ u $\le$ 2.
I dont understand the limits of the integration over v which is most likely calculated by
g(u) = $\int_0^u$ dv for 0 $\le$ v $\le$ 1, and $\int_u^2$ dv for 1 $\le$ v $\le$ 2
When drawing the graph of u on an x and y grid, I cant figure out why the limits of v go up to 2 and why they break at u. Can anyone explain the limit