Formula Sheet - Common Continuous Random Variables...

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Probability Cheat Sheet (The Legal Version!) Basic Probability Formulas Word Operation General Rule Special Case, Rule Or Add = ( )+ ( )- ( ) PA B P A P B P A B Mutually Exclusive, = ( )+ ( ) PA B P A P B And Multiply = ( ) PA B PABP B Independent, = ( ) ( ) PA B P A P B Not Subtract = - ( ) PA' 1 P A N/A Common Discrete Random Variables Name (Parameters) Lives on… pmf, or ( = ) P X x ( ) E X ( ) Var X (to get ( ) SD X , take the square root of this!) ( , ) Binomial n p { , , …, } 0 1 n = - - fx nxpx1 pn x np ( - ) np 1 p Poissonλ { , , , …} 0 1 2 = - ! fx e λλxx λ λ ( ) Geometric p { , , …} 1 2 = - - fx 1 px 1p 1p - 1 pp2 Negative ( , ) Binomial r p { , + , …} r r 1 = - - - - fx x 1r 1pr1 px r rp ( - ) r 1 p p2 ( , , Hypergeometric n G ) N , ,… , 0 1 minn G = - - fx GxN Gn xNn nGN - - - nGN GN2N nN 1 Note: the binomial coefficient in some of the pmf’s can be calculated on a calculator (the symbol should be something like nCr ), or you can calculate it directly by using = ! ! - ! nx n x n x , where != - - ⋯ ( ) n nn 1n 2 32 1 . Common Continuous Random Variables
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Unformatted text preview: . Common Continuous Random Variables Name (Parameters) Lives on… pdf cdf, or ( ≤ ) P X x ( ) E X ( ) Var X (to get ( ) SD X , take the square root of this!) Exponentialλ , ∞ =-fx λe λx = - -Fx 1 e λx 1λ 1λ2 ( , ) Uniform a b , a b =-fx 1b a = --Fx x ab a + a b2-b a212 ( , ) Weibull λ β , ∞ =--fx λβλxβ 1e λxβ Trust me, you don’t want to work with this directly! + 1λΓβ 1β +-1λ2Γβ 2β + Γβ 1β2 ( , ) Gamma α λ ,∞ =-( ) -fx λαxα 1Γ α e λx αλ αλ2 ( , Normal μ σ2 )-∞, ∞ You can just use the table or a calculator to get these values…don’t try it by hand unless you REALLY want to! μ σ2 ( ) t df-∞, ∞ Depends on the degrees of freedom Note: the gamma function ( ) Γ α is equal to ∞--0 xα 1e xdx , but when α is a positive integer, we get the much easier form of = - ! Γα α 1...
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