We say follows a Student’s t-distribution, , with degrees of freedom, if can be written as a ratio of two independent Random Variables, and .

Therefore, where

Reminder that as you’ve seen in the Chi-Squared Distribution

Support of T: Expectation and Variance

  • , since is symmetric around


For large , we use a Z-Table, since as ,


What’s the difference between this and Chi-Squared?

A T-Table is symmetric around it’s mean, which a Chi-Square Distribution is not.