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# class03_10 - 1.017/1.010 Class 10 Some Common Probability...

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Unformatted text preview: 1.017/1.010 Class 10 Some Common Probability Distributions Some common continuous PDFs and CDFs Each depends on a few distributional parameters 1. Uniform (distributional parameters a,b ) : b x a a b a x a x F a b x f x x ≤ ≤ − − + = − = ; ) ( 1 ) ( 12 ) ( ) ( 2 ) ( 2 a b x Var b a x E − = + = 2. Exponential (distributional parameter a ) : ; exp 1 ) ( exp 1 ) ( ≥ − − = − = x a x x F a x a x f x x 2 ) ( ) ( a x Var a x E = = 1 3. Univariate Normal (Gaussian) (distributional parameters σ µ , ) : tabulated form, closed no ) ( 2 ) ( exp 2 1 ) ( 2 2 = − − = x F x x f x x σ µ π σ 2 ) ( ) ( σ µ = = x Var x E 4. Lognormal (distributional parameters x x ln ln , σ µ ) : tabulated form, closed no ) ( 2 ) (ln exp 2 1 ) ( 2 2 = ≥ − − = x F x x x x f x x σ µ π σ [ ][ 1 ) exp( 2 exp ) ( 2 1 exp ) ( 2 ln 2 ln ln 2 ln ln − + = + = x x x x x...
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class03_10 - 1.017/1.010 Class 10 Some Common Probability...

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