Let X1, ,Xn be a random sample from a distribution with density f(x,) 33x2 for 0 x (i) Find the MLE of (ii) Find the MME of (iii) Approximate the distribution of T 3X (iv) Obtain the MSE of Ta aX as an estimator of

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Question: Let X1, ...,Xn be a random sample from a distribution with density f(x,) = 33x2 for 0 x . (i) Find the MLE

Let X1, ...,Xn be a random sample from a distribution with density f(x,θ) =

3θ−3x2 for 0 ≤ x ≤ θ. (i) Find the MLE of θ. (ii) Find the MME of θ. (iii) Approximate the distribution of T = 3X. (iv) Obtain the MSE of Ta = aX as an estimator of θ.

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