Solution:
Possible sample of size 2 with replacement={(1,3)(3,8)(1,8),(1,1),(3,3),(8,8)}
Sample means for these samples={2,5.5,4.5,1,3,8}
(1): Mean of sample means=(2+5.5+4.5+1+3+8)/6=4
Population mean=(1+3+8)/3=4
Population variance,σ2=3(1−4)2+(3−4)2+(8−4)2=326
(2): The variance of the sampling distribution of means,σx2=n(N−1)σ2(N−n)
=2(3−1)326(3−2)=613
(3): The standard deviation of the sampling distribution,σx=613
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