00:01
So we've just got a question about expectation here.
00:02
So we want to show that the expectation of x minus mu over sigma is equal to zero.
00:08
Now by linearity of expectation, this is just equal, we can pull the one over sigma out the front because that's just a constant.
00:13
And then we get the expectation of x minus the expectation of mu.
00:17
Now mu is just a constant.
00:18
So the expectation of mu is just itself.
00:21
And the expectation of x is it's mean.
00:24
And we're told in the question that it's mean is mu.
00:26
So we've got mu minus mu and that's clearly zero.
00:28
So yeah, we're using that the expectation of x is mu, and the variance of x is sigma squared.
00:37
That's what we're told in the question.
00:40
So we then want to show that the expectation of this quantity squared is one.
00:44
Now, this quantity squared, if we expand that out, we get x squared minus 2x mu plus, sorry, plus mu squared over sigma squared...