Exercise

# Probabilities under the t-distribution

We can use the `pt()`

function to find probabilities under the t-distribution. For a given cutoff value `q`

and a given degrees of freedom `df`

, `pt(q, df)`

gives us the probability under the t-distribution with `df`

degrees of freedom for values of `t`

less than `q`

. In other words, \(P(t_{df} < T)\) = `pt(q = T, df)`

.

Instructions

**100 XP**

- Find the probability under the t-distribution with 10 degrees of freedom below \(T = 3\).
- Find the probability under the t-distribution with 10 degrees of freedom above \(T = 3\).
- Find the probability under the t-distribution with 100 degrees of freedom above \(T = 3\).
- How do the last two probabilities compare? Why?