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Thanks a lot. Appreciate it.

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The following estimators for a use a simple random sample (X, ~- i.i.d)
with n observations: :
ALL=
ME
nXi
FXi
As =
(Xi + Xn)
5. Which of these estimators are unbiased? [Provide a short formal proof.]
6. If possible, compare these estimators with respect to their relative effi-
ciency. [Provide a short formal proof.]
7. Which of these estimators are consistent? [Provide a formal proof.]
Out of n = 25 interviewed workers only the first 6 and the last 2 are
willing to strike.
8. Compute the estimates v1, v2 and va.
9. Which of the three estimates is the best one? Explain your answer.
10. What simple prediction about the total number of workers willing to
strike would you make?

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1 Problem 1 - Properties of Estimators
A company with / = 5000 workers would like to gauge the share (x) of
workers who are willing to strike.
Let X,: "The number of workers willing to strike per i-th worker". Denote
* the probability that worker i is willing to strike.
Let X = E X; : " The number of workers willing to strike in a simple
random sample of size n."

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