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Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn...

Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn be the maximum of X1, X2, ..., Xn.

(a) Give the pdf of Yn.

(b) Find the mean of Yn.

(c) One estimator of θ that has been proposed is Yn. You may note from your answer to part (b) that Yn is a biased estimator of θ. However, cYn is unbiased for some constant c. Determine c.

(d) Find the variance of cYn, wherec is the constant you determined in part (c).

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