[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 continuous random variable with values exponentially

distributed over [math][0,\infty)[/math] with parameter [math]\lambda = 0.1[/math].

• Find the mean and variance of [math]X[/math].
• Using Chebyshev's Inequality, find an upper bound for the following probabilities: [math]P(|X - 10| \geq 2)[/math], [math]P(|X - 10| \geq 5)[/math], [math]P(|X - 10| \geq 9)[/math], and [math]P(|X - 10| \geq 20)[/math].
• Calculate these probabilities exactly, and compare with the bounds in (b).