Assuming a computer is available, investigate the probabilities of an “outlier” for a t-random variable and a normal random variable. Specifically, determine the probability of observing the event {|X| ≥ 2} for the following random variables:

(a) X has a standard normal distribution.

(b) X has a t-distribution with 1 degree of freedom.

(c) X has a t-distribution with 3 degrees of freedom.

(d) X has a t-distribution with 10 degrees of freedom.

(e) X has a t-distribution with 30 degrees of freedom.