Chebyshevs inequality states that for any random variable X with mean and variance 2 ,

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Chebyshev’s inequality states that for any random variable X with mean μ and variance σ2, and for any positive number k, P(|X − μ| ≥ kσ) ≤ 1/k2. Let X ∼ N(μ, σ2). Compute P(|X −μ| ≥ kσ) for the values k = 1, 2, and 3. Are the actual probabilities close to the Chebyshev bound of 1/k2, or are they much smaller?

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