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

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Statistics

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 thatour parameter p of interest is the proportion of marbles in the jarthat are green. We will be allowed to take three marbles out thejar (all at once, without replacement). We will estimate p bylooking at ˆp, the proportion of marbles in our sample that aregreen.

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

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

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