/sci/ - Science & Math

>>11956790
PDF is [math]f_Z(z) = \int_{-\infty}^\infty f(x)f(z-x)dx[/math] (convolution formula). The function [math]f(x)[/math] is a piecewise function
[eqn]f(x) = \begin{cases}1 & 0<x<1,\\ 0 & \text{otherwise.}\end{cases}[/eqn]
So you have to sit down and then ask what exactly is
[eqn]f(x)f(z-x),[/eqn] In particular, it is just another piecewise function taking values of either 0 or 1, but the region where it is 1 will depend the exact [math]z[/math] value, and this gives you the bounds for integration. You will have 2 cases, so you need to integrate 2 different cases, each giving you either the left side or the right side of the triangle. There is a third case, but it is 0.

I've done probability many times, and I really hate this example. You're probably using Ross too.