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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 correct option(s) is/are


Correct Answer
A
μ=3
Your Answer
B
μ=5
Correct Answer
C
λ=3
Your Answer
D
λ=5

Solution

The correct options are
A μ=3
C λ=3
Given 10i=1(xi5)=10
Mean of the observations (xi5)=1010=1 
Hence mean of the observations  (xi3)=(old mean)+2

μ=1+2=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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