131A_1_Probability_of_Gaussian_pdf_and_Chebyshev_Inequality

131A_1_Probability_of_Gaussian_pdf_and_Chebyshev_Inequality...

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Review: For a Gaussian rv X ~ N( μ , σ 2 ), we are able to evaluate the probability around the mean μ . P(|X- μ | 3 σ ) = P( μ -3 σ≤ X ≤μ +3 σ ) = P(-3 (X- μ )/ σ≤ 3) = Φ (3) - Φ (-3) = 0.9974, P(|X- μ | 3 σ ) = 0.0026; Probability of Gaussian pdf (1) μ μ - 2 μ+2 μ + 3 μ - 1 μ - 3 μ+1 0.9974
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Probability of Gaussian pdf (2) P(|X- μ | 2 σ ) = 0.9544; P(|X- μ | ≤σ ) = 0.6826; P(|X- μ | 2 σ ) = 0.0456; P(|X- μ | ≥σ ) = 0.3174 . μ μ - 2 μ+2 μ + 3 μ - 1 μ - 3 μ+1 0.9544 μ μ - 2 μ+2 μ + 3 μ - 1 μ - 3 μ+1 0.6826
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Chebyshev inequality (1) Given specific pdf’s (e.g., Gaussian pdf), we can find the probability around the mean (or its complement). For an arbitrary rv X, if we only know its mean μ and its variance σ 2 , what are such probabilities? Chebyshev Inequality
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This note was uploaded on 02/09/2011 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.

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131A_1_Probability_of_Gaussian_pdf_and_Chebyshev_Inequality...

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