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2868概率简单derivationmedium

Recovering Chebyshev from Markov

题目

Derive Chebyshev's inequality from Markov's inequality. In other words, show that for any random variable XX with mean μ\mu and variance σ2\sigma^2, \[ P(|X-\mu|\ge a)\le \frac{\sigma^2}{a^2}. \]

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