[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Let [math]X[/math] be a random variable with cumulative distribution function

[math]F[/math]. The median of [math]X[/math] is the value [math]m[/math] for which [math]F(m) = 1/2[/math]. Then [math]X \lt m[/math] with probability 1/2 and [math]X \gt m[/math] with probability 1/2. Find [math]m[/math] if [math]X[/math] is

• uniformly distributed over the interval [math][a,b][/math].
• normally distributed with parameters [math]\mu[/math] and [math]\sigma[/math].
• exponentially distributed with parameter [math]\lambda[/math].