Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X2, X3,..., Xn has the following probability density function (exe-e x! c d f(x; 0) = 0, , for x = 0,1,2,... elsewhere X₁+2X2+2X3-X4 and 6₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which 4 Let 6₁=X₁+2X₂ one of the two estimators is more efficient? What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter 8?

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A: We have given, A continuous random variable X has the following CDF: F(x) = 1 - 1x+14, x > 0.

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A: Given To prove that

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A: Answer: For the given data,

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Q: n F. De X(w) i- -X(w)

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A: Step 1: Step 2: Step 3: Step 4:

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A: The given value are EX=34, EX2=35, EY=38, EY2=15 and EXY=310.

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