Probability and Statistics Explain why Theta X1X22 arctanX3

1. Suppose that X1, X2, X3 are identically distributed and independent random variables. Explain why a. Xs are ilentically distributed and #2 (X1 1X2)2 arc tan(X3) is a statistic and a random variable. Your explanation should include what a statistic is in genera

Solution

A statistic is the characterstic of sample, which does not depend on population parameters.

here X1, X2, X3 are three random variable that are iid\'s.

And theta is a function of these independent random variables.

and it doesn\'t depend o population parameter thus theta is also a statistic.

(A statistic is always independent of population parameter, it is always constructed with the sample characterstics.)