# T distribution and F distribution

Please see attached problem, and please explain all aspects of both problems involving T and F distributions.

a) Z is a standard normal random variable, and U is distributed as X(v)^2. Z and U are independent. State the distribution of T = Z/sqrt(U/v) . What is the distribution of T^2?

b) Y is a random variable distributed as F(1,5) . Use your answer to part (a), together with the tables of the t (not the F) distribution, to find P(Y > 4) . Also find the value of c such that P(Y > c) = 0.01.

https://brainmass.com/statistics/f-test/distribution-distribution-465245

#### Solution Preview

a) Z is a standard normal random variable, and U is distributed as X(v)^2. Z and U are independent. State the distribution of T = Z/sqrt(U/v) . What is the distribution of T^2?

T, by definition, is called the student t distribution of degrees of freedom v (where v is the d.f. of the chi square). Furthermore, if T is a student t distribution of d.f. = ...

#### Solution Summary

This solution helps with questions involving parametric tests, specifically T distributions and F distributions. Step by step calculations are given along with explanations.