(Requires Appendix material)If X and Y are jointly normally distributed and are uncorrelated,
A)then their product is chi-square distributed with n-2 degrees of freedom
B)then they are independently distributed
C)then their ratio is t-distributed
D)none of the above is true

Question

Quizplus · Accepted Answer

If X and Y are jointly normally distributed and are uncorrelated, it does not necessarily mean that their product is chi-square distributed or that their ratio is t-distributed. However, it does imply that they are independent, since the covariance between X and Y is 0. Therefore, choice B is the correct answer.

(Requires Appendix Material)If X and Y Are Jointly Normally Distributed