All the samples of size 2:
(2,5),xˉ=3.5(2,7),xˉ=4.5(2,8),xˉ=5(2,9),xˉ=5.5(5,7),xˉ=6(5,8),xˉ=6.5(5,9),xˉ=7(7,8),xˉ=7.5(7,9),xˉ=8(8,9),xˉ=8.5
The sampling distribution
P(xˉ=3.5)=P(xˉ=4.5)=P(xˉ=5)=P(xˉ=5.5)=P(xˉ=6)==P(xˉ=6.5)=P(xˉ=7)=P(xˉ=7.5)=P(xˉ=8)=P(xˉ=8.5)=0.1
Histogram:
EX=0.1(3.5+4.5+5+5.5+6+6.5+7+7.5+8+8.5)=6.2EX2=0.1(3.52+4.52+52+5.52+62+6.52+72+7.52+82+8.52)=40.75DX=EX2−(EX)2=40.75−6.22=2.31σX=DX=2.31=1.51987
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