00:01
So this question, we're told that x is normally distributed, and we're told that the mean is one and the standard deviation is also one.
00:11
And we have y is e to the x.
00:14
Now we want the expected value of y cubed.
00:17
So that's the expected value of e to the 3x, which is the integral from minus infinity to infinity, 1 over 2, root 2 pi and then sigma squared, which is just 1.
00:31
E to the 3x, e to the minus 1 half, x minus 1 squared, the x.
00:41
So this is 1 over root 2 pi, integral from minus infinity to infinity.
00:47
And now what we need to do is complete the square.
00:50
So we have e to the minus a half.
00:53
Now we've got an x squared minus 2x plus 1, but we also have 3x, which is minus a half of minus 6x.
01:04
So we have minus 8x here now...