In an SRSWR, a population unit can appear in the sample anywhere between 0 and n times.

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 appears in the sample,

And

1. Argue that the joint distribution of Q1,Q2, . . . ,QN is multinomial with n trials and

p1 =p2= · · · =pN =1/N.

2. Using (a) and properties of the multinomial distribution, show that E[ṫ]=t.

3. Using (a) and properties of the multinomial distribution, compute V[ṫ ].

Distribution
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