statistics ques

[Sinistral]

[wolverine]

it can be verified for any value of n
take n=2
X1,X2,X3,X4 be the rv

so we will find V(X1-X2+X3-X4)= V(X1+X3-(X2+X4))

= V(X1+X3) + V(X2+X4) - 2COV(X1+X3,X2+X4)

= V(X1)+V(X3) +2COV(X1,X3) + V(X2) +V(X4) + 2COV(X2,X4) -    2[COV(X1,X2)+COV(X1,X4)+COV(X2,X3)+COV(X3,X4)]....egn 1\


given V(Xi)=4 and cov(Xi,Xj)=3  putting dese  values in 1 we get

4+4+ 2*3 +4 +4 + 2*3 -2(3+3+3+3)
= 28-24=4

which equals 2n...option b

[Amit Goyal]

Solution is attached:
sol_stat.png

[Sinistral]

thank you both of you. I realised I hadnt studied unbiasedness & i jumped to this ques.