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# UF - STA 3032 - Engineering Stats 3032 EXAM 2 Typed Study GUIDE -

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UF - STA 3032 - Engineering Stats 3032 EXAM 2 Typed Study GUIDE -

##### Uploaded: 03/05/2018
This preview shows pages 1 - 3 of a 11 page document. to view the rest of the content Exam 2 study guide- class notes 43- TBD Keywords Common Discrete Distributions: Bernoulli: (X~Bernoulli P) will the result x be: yes or no X= 1 success; Eq: p X=0 failure; Eq: (1-p) PMF: p(x)=  1− p ¿ 1− x P x ¿ P is Between 0 and 1 E(x)= P Variance: V(x)= p(1-p) Binomial: (X~(n, p): P how many times x occurs x = success n= number if trials (Each trial is independent) p= success probability PMF: p(x)  ( n
x
) p x ( 1− p ) n− x E(X): np V(X): np(1-p) At most :  ------------Part2 of Binomial’s for  ^ P value ---: find probability at least that there are at least x results out of given trials-- ^ P/n  : proportion of success (^) = p (^) p ( 1− p ) n R: Pbinom (x,n,p) Geometric: X~ Geom( p ) p trials needed to get to X get result. PMF: p(x) = p ( 1− p ) x−1 E(X) = 1/p V(x)=  ( 7− p ) P 2 R: dgeom(4,p) *failures before succes* Negative Binomial: X~ NB(r,p) number of trials up to rth success, including r. PMF:  p ( x ) = ( x−1
r−1
) p r ( 1− p ) xr E(X): r/p V(X) =  r ( 1− p ) p 2 R: dbinom (x,r,p) *  sum of geometric* Poisson: X~ Poisson ( λ ). Occurrence over time PMF: P(x)=  λ x λ x! E(x)=V(x) R: dpois( λ x t) -------------- Estimated Value  ^ λ -------------------------- ^ λ  = X/t ^ σ = ^ λ T Uniform: X~Uniform [a,b] P= integrate PDF PDF: f(x) = 1/(b-a) E(X): (a+b)/2 V(X):  ( ba ) 2 12 R: 1-punif (a,,b) Normal:  Anything can be normal if you have a lot of trials X~ N  ( μ ,σ 2 ) . PDF: f(x)=  1 σ π 1 2σ 2 ( x− μ ) 2 Random Variable Form: Multiply by  σ  add  μ E(x)=  μ   V(x)= σ 2 --------Standard Normal: Z~N (0,1)-------------- CDF: get in standard form, split, R Standard Normal:  z= xμ σ Example: Standard Normal Form:           1. Subtract  μ  from everything                                        2. divide everything by σ                                             Split:                       p(a ¿ Z ¿ b)= b-a R:                      pnorm(a) -pnorm (b) R: pnorm(a) -pnorm (b) R(shortcut if values are given): qnorm( p,b,a) Mean = 0 Variance = 1 E(x)= b V(x) =  a 2 Central Limit Theorem  ´ x N ( μ , σ 2 n )

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##### Uploaded: 03/05/2018
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