4/a).
∑Xi=1, ∑Yi=2 and “n=5”, => ∑(Xi+Yi) = ∑Xi + ∑Yi = 1+2 = 3, => ∑(Xi + Yi) = 3.
b).
∑(Xi-2*Yi) = ∑Xi - ∑2*Yi = ∑Xi – 2*∑Yi = 1 – 2*2 = (-3), => ∑(Xi - 2*Yi) = (-3).
c).
∑(Xi - 1), => ∑Xi - ∑1 = 1 – n = 1-5 = (-4), => ∑(Xi - 1) = (-4).
5/i).
=> X bar = (1/n)*∑Xi = 1, => ∑Xi = 1*n = 100, => ∑Xi = 100.
ii).
=> ∑(Xi – X bar) = ∑Xi – ∑X bar = ∑Xi – X bar*∑1 = 100 – 1*n = 100 – 1*100 = 0.
=> ∑(Xi – X bar) = 0.
and
=> ∑(X bar + 1) = ∑X bar + ∑1 = X bar*∑1 + n = 1*n + n = 2n = 200, => ∑(X bar + 1) = 200.
4. Suppose Σί, 1 Xi-1, ΣΙ-, x-2, and n-5. Evaluate the followings: a) Σί-1[Xi + X)...
4. Suppose Ση.i X, = 1, Σι Yī = 2, and n = 5. Evaluate the followings: a) Σ_1X itk] b)
5. Let X-1Ση-1 Xi : 1 with n-100. (i) Obtain Ση: 1 Xp (ii) Evaluate Ση-1(Xi-X] and
4. Let X1,X2, x 2) distribution, and let sr_ Ση:1 (Xi-X)2 and S2 n-l Σηι (Xi-X)2 be the estimators of σ2. (i) Show that the MSE of S" is smaller than the MSE of S2 (ii) Find ElvS2] and suggest an unbiased estimator of σ. n be a random sample from N (μ, σ
2. Let 'n ,n > l be a sequence of r.v.s such that E[Xi] μί and Var(X) σ for i-: 1, 2, , and Cov(Xi, Χ.j) Ơij for i J. Let {an ,n 1) and (bn, n 1) be the sequences of real numbers. Write down the expressions for i-l (i,Xi, Xi), Cov every i and Ơij 0 for every i j, state Var(Σί ! així), Coy(Σ, aixi, xi),
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