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 P(X a) 0 + a

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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Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

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Question Posted: Oct 27, 2023 02:26 AM

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Let X be a random variable with EX = 0 and Var(X) = 2 . We

Question:

P(X ≥a) ≤ 0² σ² + a²

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To prove the onesided Chebyshev inequality we can use the following technique Given X is a random va...View the full answer

Introduction To Probability Statistics And Random Processes

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