Definition of Student's T -Distribution

Let

T = Z/sqrt(U/r)

where

a. Z is N (0, 1),

b. U is chi^2 (r) ,

c. Z and U are independent.

Then T has a Student- T distribution with r degrees of freedom. (We usually drop the word Student and simply say the T distribution.)

1. Graph the p.d.f. of T for several values of r . Solution

2. Find the p.d.f. of T theoretically. Solution

3. Simulate observations of " T " when some hypotheses are not satisfied. Solution

4. Simulate observations of " T " and "almost T. " Solution