Suppose thatnbspx1 x2 is a sequence of random variables


  • Suppose that X1, X2, . . .is a sequence of random variables with E(Xt28 and E(Xt)=µ.
  • a. If X1, X2, . . .is iid with E(Xi28 and EXi=µ, where µis known, whatis the minimum mean squared error predictor of Xn+1in terms of X1, . . . , Xn?
  • b. Under the conditions of part (c) show that the best linear unbiased estimator of µin terms of X1, . . . , Xnis X¯ =(X1 + · · · + Xn)/n. (µˆ said to be anunbiased estimator of µif Euˆ=µfor all µ.)
  • c. Under the conditions of part (c) show that X¯ is the best linear predictor of Xn+1 that is unbiased for µ.
  • d. If X1, X2, . . .is iid with E(Xi28 and EXi, and if S0=0, Sn=X1 + · · · + Xnn=1,2, . . ., what is the minimum mean squared error predictor of Sn+1in terms of S1, . . . , Sn?

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Basic Statistics: Suppose thatnbspx1 x2 is a sequence of random variables
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