(Lamperti) Let [math]X[/math] be a non-negative random variable. What is the best upper bound you can give for [math]P(X \geq a)[/math] if you know

• [math]E(X) = 20[/math].
• [math]E(X) = 20[/math] and [math]V(X) = 25[/math].
• [math]E(X) = 20[/math], [math]V(X) = 25[/math], and [math]X[/math] is symmetric about its mean.

Notes