Potential outlier

Suppose the pdf  is symmetric about 0 with cdf . Show that the probability of a potential outlier from this distribution is  Use this to obtain the probability that an observation is a potential outlier for the following distributions.

(a) The underlying distribution is normal. Use the N(0, 1) distribution.

(b) The underlying distribution is logistic; that is, the pdf is given by

(c) The underlying distribution is Laplace, with the pdf