Mathematics, 10.02.2020 22:26 tyresharichardson29
(Requires probability.) In an SRSWR, a population unit can appear in the sample anywhere between 0 and n times. Let Qi = number of times unit i appears in the sample, and ˆt = N n N i=1 Qiyi. a Argue that the joint distribution of Q1,Q2, . . . ,QN is multinomial with n trials and p1 =p2= · · · =pN =1/N. b Using (a) and properties of the multinomial distribution, show that E[ˆt ]=t. c Using (a) and properties of the multinomial distribution, find V[ˆt ].
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