Let [math]X[/math] be a continuous random variable with values unformly distributed over the interval [math][0,20][/math].

• Find the mean and variance of [math]X[/math].
• Calculate [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] exactly. How do your answers compare with those of Exercise? How good is Chebyshev's Inequality in this case?