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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 = ER Xi : " The number of workers willing to strike in a simple
random sample of size n."
1. State the distribution of the random variable X, [Write down the dis-
tribution model and parameter(s).]
2. Derive E[X;] and V[X ] as a function of .
3. State the distribution of the random variable X [Write down the dis-
tribution model and parameter(s).]
4. Derive E[X] and V[X] as a function of n.

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