Suppose that a sample of size 4 is taken from a population with mean µ and variance 2 . Let x, be the sample mean for that sample. Suppose that another sample of size 9 is taken from the same population. Define its sample mean as Xo. Now we will define the estimator e = kX4 + (1 – k) X9 : a. Show that O is an unbiased estimator of e for all possible values of k . b. Express the variance of O in terms of k and o2. c. Determine the value of k that minimizes V [0].

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A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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Q: 3. Suppose that E(X) = E(X2) = E(X2) = µ, Var(X) = 7, Var(X2) = 13, and Var(X3) = 20. %3D %3D %3D…

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Q: 8. Given two estimators X1 and X2 for a population mean, E[X1] = 6, V[X1] = 4, and V[X2] = 5. If the…

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Q: 2. For a population with u = 40 and o = 5, compute the z-score corresponding to each of the…

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Q: An SRS of n = 20 observations is collected from a normal population to test H0 ∶ µ = 15 against Ha ∶…

A: From the given information, μ=15t=-2.06 n=20 df=n-1=20-1=19

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.