00:01
Here on this problem, we were told that the expected value of x minus 1 squared is equal to 10, and the expected value of x minus 2 squared is 5.
00:12
Now, we would like to use these two values in order to find mu and sigma square.
00:17
Now, first, let's foil x minus 1 squared out, giving us x squared minus 2x plus 1 is 10, and similarly over here on the other way, we have the expected value of x squared minus 4x plus 4 is equal to 5.
00:40
Now here on the left, this tells us that the expected value of x squared, minus two times the expected value of x, plus one is 10.
00:50
And on the right, we have the expected value of x squared, minus four times the expected value of x, plus four, is equal to five.
01:01
Now here, we have a system of equations that we can solve.
01:06
And so rather than e of x squared, let's treat that like a.
01:10
Rather than e of x, let's call that mu, and for our mean, that's what it represents.
01:17
And the same thing here on the other.
01:18
We have a minus 4 mu plus 4 is equal to 5...