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Question

Let the observations xi(1i10) satisfy the equations, 10i=1(xi5)=10 and 10i=1(xi5)2=40. If μ and λ are the mean and the variance of observations, (x13),(x23),...,(x103), then the ordered pair (μ,λ) is equal to :

A
(6,3)
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B
(3,6)
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C
(3,3)
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D
(6,6)
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Solution

The correct option is C (3,3)
10i=1(xi5)=10
10i=1xi50=10
10i=1xi=60

μ=10i=1(xi3)10=10i=1xi3010=3

Variance is unchanged, if a constant is added or subtracted from each observation
λ=Var(xi3)=Var(xi5)
=10i=1(xi5)210⎜ ⎜ ⎜ ⎜10i=1(xi5)10⎟ ⎟ ⎟ ⎟2
=4010(1010)2
=3

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