Introduction to Probability · Problem 8.2.2

Central Limit Theorem — Grinstead & Snell

Mathematics — Probability · law-of-large-numbers-continuous

Problem

Let XX be a continuous random variable with values uniformly distributed over the interval [0,20][0, 20]. (a) Find the mean and variance of XX. (b) Calculate P(∣X−10∣≥2)P(|X - 10| \geq 2), P(∣X−10∣≥5)P(|X - 10| \geq 5), P(∣X−10∣≥9)P(|X - 10| \geq 9), and P(∣X−10∣≥20)P(|X - 10| \geq 20) exactly. How do your answers compare with those of Exercise 1? How good is Chebyshev's Inequality in this case?

Related theory

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