Suppose that X1 and X2 are independent random variables having a common mean μ. Suppose also that Var(X1) = σ21 and Var(X2) = σ22. The value of μ is unknown, and it is proposed that μ be estimated by a weighted average of X1 and X2. That is, λX1 + (1 − λ)X2 will be used as an estimate of μ for some appropriate value of λ. Which value of λ yields the estimate having the lowest possible variance? Explain why it is desirable to use this value of λ.
Answer to relevant QuestionsIn Example 4f, we showed that the covariance of the multinomial random variables Ni and Nj is equal to −mPiPj by expressing Ni and Nj as the sum of indicator variables. We could also have obtained that result by using the ...Show that Y = a + bX, then One ball at a time is randomly selected from an urn containing a white and b black balls until all of the remaining balls are of the same color. Let Ma,b denote the expected number of balls left in the urn when the ...Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give two exams, one to a class of size 25 and the other to a class of size 64. (a) Approximate the ...Fifty numbers are rounded off to the nearest integer and then summed. If the individual roundoff errors are uniformly distributed over (−.5, .5), approximate the probability that the resultant sum differs from the exact ...
Post your question