Question

Suppose that X is a random variable with mean and variance both equal to 20. What can be said about P{0 ≤ X ≤ 40}.

Answer 1

Answer:

$P(0 \leq X \40) = \frac{19}{20}$

Step-by-step explanation:

We know that:

$P(|X - 20| < 20) + P(|X - 20| \geq 20) = 1$

So

$P(0 \leq X \leq 40) = P(0-20 \leq X-20 \leq 40-20) = P(-20 \leq X \leq 20) = P(|X - 20| \leq 20)$

$P(|X - 20| \leq 20) = 1 - P(|X - 20| > 20) = 1 - \frac{20}{20^{2}} = \frac{19}{20}$

So

$P(0 \leq X \40) = \frac{19}{20}$