00:01
So to begin here, i'll note that the variance can be thought of as being equal to the expected value of the square of the expected value.
00:14
Or, pardon me, it's equal to the expected value of the square of x minus the expected value of x.
00:21
So, when we're considering our different options, if we look at option c, the expected value of x1 minus mu squared plus x2 minus mu squared plus dot dot dot plus xn minus mu squared all over n is going to be equal to 1 over n times the expected value.
00:58
Of x1 minus mu squared plus x2 minus mu squared plus dot dot up to x n minus mu which in turn would be equal to 1 over n times the expected value of x1 minus mu squared plus the expected value of x2 minus mu squared plus dot dot dot dot but we'd have that each one of these expected values, x1 minus mu and x2 minus mu and so on, those individual expected values would be equal to the expected value of just x, generally speaking, minus the population mean value squared.
01:57
So we have that this is going to be equal to 1 over n times, well, how many times are we writing out this expected value of x1, x2, etc, minus, mu then squared, well we would be doing that n times...