Suppose you are asked to estimate the value of the target parameter theta, based

Question

Suppose you are asked to estimate the value of the target parameter theta, based on a random sample of data X_1, X_2, ...., X_n from the population of values. You then compute a statistic from this sample. theta Consider the random variable A = theta * theta Which of the following statements is not part of the 'Pivotal Quantity' check of A? A is a function of a statistic computed from the random sample A is not a function of the target parameter theta A is a function of the target parameter theta f_A(a) is free of the target parameter theta

Explanation / Answer

answer is  c. A is function of the target parameter .

In statistics, a pivotal quantity or pivot is a function of observations and unobservable parameters whose probability distribution does not depend on the unknown parameters. Random variable Q(X,) is a pivotal quantity if the distribution of Q(X,) is independent of all unknown parameters.

so right choice is c. A is function of the target parameter .

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