# Chebychev and/or Markov

Discrete Mathematics Level 5

Let $$X$$ be a random variable with a finite expected value $$\mu = E(X)$$ and a finite variance $$\text { Var (X) } = \sigma^2 > 0$$. Then the probability $$P (\mu -3\sigma < X < \mu + 3\sigma) \ge \frac{a}{b}$$ with absolute certainty. Find this maximum value $$\frac{a}{b}$$ with $$a, b$$ coprime positive integers. Submit $$a + b$$.

×