Suppose that x1, ... x10 are a random sample of 10 observations from the following probability mass function, where 0 less than theta less than 1 is a parameter:
| x |
0 |
1 |
2 |
3 |
| p(x) |
2theta/3 |
theta/3 |
2(1-theta)/3 |
(1-theta)/3 |
The random sample yielded the observations (3,0,2,1,3,2,1,0,2,1).
a. Calculate the method of moments estimator and the maximum likelihood estimator of theta.
b. Compute the mean squared error of the MOM estimator.