Question

Estimators A researcher is granted access to dataset from a local NGO which operates in Morocco. The datset records Moroccan households electricity consumption, emasured in kilowatt/hour (kWh). The sample is i.i.d and the sample size is n = 850. The researcher is interested in the probability that a household consumption is between 2100 kWh and 2400 kWh. a) Propose a consistent estimator for the probability that a household consumption is between 2100 kWh and 2400 kWh. b) The researcher also estimates the sample average for electricity consumption. What is the probability that the estimated sample average is equal to 2250 kWh?

Answer 1

a) The propose estimates that a household consumption is betaloon 2000 klein and 2400 kketh is X = ECA) and it is conbaised but it does not converge to any value However, if a sequence of estimate is umbaised and converges to a value Then it is consistent at it most converge to the correct value Therefore Ho have PC 2100 kish ex e 2400 kish) b) To get 6 Asso 6 = 1 850 tooe 850-1 X-4 6 2100 2250 ext 2400 - 22so (1 1 - 150 x 150