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Three randomly selected households are surveyed. the numbers of people in the households are 1,3,8 assume that samples of size n =2 are randomly selelcted with replacement from the population of 1,3,8. Listed below are the nine different sample 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10 find the variance of each of the nine samples then summerize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values

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okpalawalter8

The estimator sample proportion is mathematically unbiased

What is the estimator sample proportion?

Generally, the equation for is  mathematically given as

Population sample \mu=1.3

The sample to sample proprotion table will have

first column= 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10

Second coumn= 0,0,0.5,0,0,0.5,05,0.5, total 3

The probability distribution of the distinct variance values table will have

p row=0,0.5,1, Total

probability row= 4/9, 4/9, 1/9, 1

In conclusion, The mean sample

x=3/9

x=1.3

Where

population sample \mu=1.3

\mu= x

Therefore the estimator sample proportion is unbiased for population mean

Read more about probability

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