00:02
Okay, so here we're talking about a uniform random variable, which means that any value between its endpoints is equally likely to happen.
00:12
So what that means for us is that our density function is a rectangle like this.
00:18
And if we want to find the cumulative density function, cdf, which we denote f of x, it describes how much probability we've accumulated up to a point.
00:33
So if we have this point x over here, it's how much probability is up till there.
00:39
So if we want to figure out how much probability is there, knowing that this is a valid pdf and the area of the rectangle is one, we can just find out how much area is in this portion.
00:50
And so the area of the shaded portion is just going to be the height times the length.
00:58
So the length is easy.
01:01
We know we're at a point x.
01:03
We know it starts at a.
01:06
So our length is actually just going to be x minus a.
01:09
Think if this was, say, 10 and our a is 8, we know that the distance between them is 2...