Q.

Let x1, x2,......x10 be ten observations such that i=110xi2=30,i=110xiβ2=98,β>2 and their variance is 4/5. If μ and σ2 are respectively the mean and the variance of 2(x1–1) + 4β, 2(x2–1) + 4β, ....., 2(x10–1)+ 4β, then βμσ2 is equal to :

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a

100

b

120

c

90

d

110

answer is A.

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Detailed Solution

45=xi210xi10245=xi21025xi2=258 Now i=110xiβ2=98i=110xi22βxi+β2=982582β(50)+10β2=98(β8)(β2)=0β= or β=2  (as β>2)β=8
Now,
=2x11+4β,2x21+4β,2x101+4β=2x1+30,2x2+30,.2x10+30μ=2(5)+30=40σ2=2245=165σ2=8×4016/5=100

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