ASM, exercise 19.11 (Review of Mathematical Statistics)
I have the 11th edition. The question reads (with simplification):
A population contains the values 1, 2, 4, 9. A sample of 3 is withdrawn without replacement from this variable. Calculate the mean square error of the median of this sample as an estimator of the population mean.
The solution is: half the time the sample median is 2 and the other half the time it is 4. The mean of the population is 4. So the MSE is 1/2*(2-4)^2=2. I don't understand the last step. Is there a Bernoulli shortcut involved.