小杜 asked in 科學數學 · 1 decade ago

高等統計學

Let X1,X2,...,Xn be a random sample from a uniform distribution on the interval (theta-1,theta+1) . theta:很像眼睛的希臘符號(打不出來)

(a)Find the method of moments estimators for theta?

(b)Is your estimator in part (a) an unbiased estimator for theta?

能的話,大概講解一下。謝謝

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  • 1 decade ago
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    The first moment of uniform distribution of interval (theta-1, theta +1) is (theta - 1 + theta + 1) / 2 = theta. It is used sample mean to estimate population mean, hence sample mean is the M.M.E. of theta.

    To check if it is an unbiased estimator, you can just take expectation of M.M.E. (sample mean in this case). That is,

    E( sample mean ) = [ E(X1) + ... + E(Xn) ] / n = theta.

    Source(s): from me
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