00:01
In order to evaluate this function here, well, to make it a probability distribution, probability density function, it needs to equal one.
00:10
And so we're going to go ahead and use a u substitution here.
00:12
So if u equals negative x over two, take the derivative of both sides, that'll give du dx equals negative 1â2, multiply the negative 2 over.
00:23
So we could say negative 2du equals dx.
00:27
And then we're going to replace this here.
00:32
So this is going to be negative 2.
00:34
Let's just put that in front, negative 2.
00:36
And then this will be du.
00:39
And then, of course, our power here is all u as well.
00:43
So that's just to the u.
00:44
So integrating, we're just going to get e to the u is the result.
00:49
And so let's rewrite that.
00:50
So that's negative 2, negative 2, k, e to the negative x over 2...