consistent estimator for the probability

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Question: Two researchers are given 2 datasets from the World Bank regarding the saving behavior of households in Kenya. The currency in Kenya is the shilling (KES). At the current exchange rate 107.850 KES = 1USD. Each of the n = 150 observation in the dataset is sampled from the same population of households but the observations contained in each dataset are not necessarily the same. Each researcher is asked to provide an estimate for the probability that a household saves more than 10,000KES a month.

a) Propose a consistent estimator for the probability that a household saves more than 10,000KES a month

b) The two researchers would also like to compute the sample average for the household savings. What is the probability that the two reaserchers will have the same estimate?

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