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 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 t c Using (a) and properties of the multinomial distribution, find V

Question: In an SRSWR, a population unit can appear in the sample anywhere between 0 and n times. Let Qi = number of times unit i

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
a. Argue that the joint of Q1,Q2, . . . ,QN is multinomial with n trials and
p1 =p2= · · · =pN =1/N.
b. Using (a) and properties of the multinomial show that E[ṫ]=t.
c. Using (a) and properties of the multinomial find V[ṫ ].

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