DB Week 8

#Question 5 page 312

Let x be a rnadom variable with \(E(X) = 0\) and \(V(X) = 1\). WHat integer value k will assure us that \(P(|X| \geq k) \leq 0.01?\)

Chebyshev’s Inequality states that \(P(|X - \mu| \geq k\sigma) \leq \frac {\sigma^2}{k^2\sigma^2} = \frac {1}{k^2}\)

Solving for \(k\)

\[\frac {1}{k^2} = 0.01 \\ k^2 * 0.01 = 1 \\ k^2 = \frac {1}{0.01} \\ k = \sqrt{100} \\ k = 10 \]