Suppose an estimator

hat(\\\\theta )_(1)

for a parameter

\\\\theta >0

has expected value

E(hat(\\\\theta )_(1))=((n\\\\theta -1)/(n+1))

and\ variance

V(hat(\\\\theta )_(1))=((\\\\theta )/(n+1))^(2)

.\ a. \ What is the bias of

hat(\\\\theta )_(1)

? Does this estimator tend to over- or underestimate

\\\\theta

?\ b.\ Is

hat(\\\\theta )_(1)

consistent? Justify your answer.\ c.\ Construct an alternative estimator, hat\\\\theta 2, that is a function of hat\\\\theta 1 and is an unbiased estimator of \\\\theta \ d. \ What is the variance of the estimator you constructed, hat\\\\theta 2? Is hat\\\\theta 2 more, or less efficient than hat\\\\theta 1?\