MAU_Finalsummarysheet

# MAU_Finalsummarysheet - MAU Summary Sheet Calculus...

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 7

MAU_Finalsummarysheet - MAU Summary Sheet Calculus...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online