Let X be a random variable with EX = 0 and Var(X) = 2 . We
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Let X be a random variable with EX = 0 and Var(X) = σ2. We would like to prove that for any a > 0, we have
This inequality is sometimes called the one-sided Chebyshev inequality. One way to show this is to use P(X ≥ a) = P(X + c ≥ a + c) for any constant c ∈ R.
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P(X ≥a) ≤ 0² σ² + a²
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Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik
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