A jar contains 2 green marbles, G1 and G2, and 4 yellow marbles, Y1, Y2, Y3,...

A jar contains 2 green marbles, G1 and G2, and 4 yellow marbles, Y1, Y2, Y3, and Y4. Imagine that we do not know this. Suppose that our parameter p of interest is the proportion of marbles in the jar that are green. We will be allowed to take three marbles out the jar (all at once, without replacement). We will estimate p by looking at ˆp, the proportion of marbles in our sample that are green.

(a) Write down the sampling distribution of ˆp, showing enough work that I can follow. (Assuming that pˆ is approximately normal is not valid in this case [why?] so don’t do it.)

(b) Is ˆp an unbiased estimator for p? Answer clearly and then explain, showing all necessary work.

Expert Solution

orchestra answered 1 year ago

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