MAU_Finalsummarysheet - MAU Summary Sheet Calculus...

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Carl Hansen Calculus definitions of statistical stuff Probability distribution function: x ) x ( F ) x ( f = ; or discrete case: ) 1 x ( F ) x ( F ) x ( f - - = Cumulative distribution function: - = x dX ) X ( f ) x ( F ; or discrete case: = = n 0 i ) i ( f ) n ( F Mean: - = = μ dx ) x ( xf ] x [ E Expectation notation: - = dx ) x ( f * ) x ( g )] x ( g [ E Variance = stdev 2 : 2 2 2 2 2 ] x [ E dx ) x ( f * ) x ( ] ) x [( E μ - = μ - = μ - = σ - Percentile (inverse cumulative probability) - - = = 1 A X 2 1 A 1 dx ) x ( f A ; = 2 A X 2 dx ) x ( f A outliers defined as 1.5 IQR out sided of QI or QIII two events may be mutually exclusive P(S) = 1, entire space 0 ≤ P(A)≤ 1 P(Ф) = 0, empty set P(A’) = 1–P(A) P(A B ) = P(A) + P(B) – P(A B ) if mutually exclusive: P(A B ) = P(A) + P(B), just adding probabilities P(A B ) =P(A)*P(B) if reliability of components are known reliab of sys Series: one breaks down, system breaks down R(system) = i R Parallel: components substitute for each other R(system) = ) R 1 ( 1 i - - remember stand by parallel Probability Distributions: Name Notation mean stdev C / D Exponential X~exp( λ) λ < = λ - 0 t e 0 t 0 ) t ( f t - < = λ - 0 t e 1 0 t 0 ) t ( F t 1/λ 1/λ Cont. Normal X~N(μ,σ) if X~N(μ,σ), then X = σ*(Z+ μ), use minitab μ σ Cont. Std Normal Z~N(0,1) Z=(X–μ)/σ 0 1 Cont. Lognormal X~lnN(θ,ω) lnX ~ N(θ,ω) 2 / 2 e ϖ + θ ( 29 ( 29 1 e e 2 2 2 - ϖ ϖ + θ Cont Weibull X~Wei(β,α) β β - - β α α β = x 1 e x ) x ( f β α - - = x e 1 ) x ( F use MCS use MSC Cont Bernoulli { } 1 , 0 X (p) f(x)=p x (1–p) x-1 n/a p ? dscr Binomial X~Bi(n,p) x n x ) p 1 ( p x n ) x ( f - - = use a sum n*p n*p(1–p) dscr Discrete X is any value in list with given probabilities for each. use minitab dscr Poisson X~Po(λt) ! x ) t ( * e x t λ λ - use a sum λt= μ λt =μ dscr Central Limit theorem: a linear combination of normal variables is normal. Any linear combination of nonnormal variables is approximately normal. Any combination of variables might also be normal. when
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This note was uploaded on 04/22/2008 for the course ENGR 2600 taught by Professor Malmborg during the Spring '08 term at Rensselaer Polytechnic Institute.

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MAU_Finalsummarysheet - MAU Summary Sheet Calculus...

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