Quiz 1

# Quiz 1 - where r=number of successes Ex p(accept)=.2 r=need...

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Jonathan Pantano Quiz 1 ISE261 -use rad(n) intervals for bar chart -a quartile is 25% of the relative frequency -variance = 1 ) ( 2 - - n x x avg i The standard deviation (s) is the square root of this. -shortcut for s= 1 / ) ( ) ( 2 2 - - n n x x i i -Box plot: smallest, lower4, median, upper4, largest4 -Permutation: P k,n = )! ( ! k n n - -Combination C k,n = )! ( ! ! ) ( k n k n k n - = N objects K at a time - ) ( ) ( ) ( ) ( B A P B P A P B A P - + = , -Conditional P(A|B)= P(AandB)/P(B) –Bayes = ) ( ) | ( ) ( ) | ( ) | ( i i A P A B P A P A B P B A P Ex) ) ( ) ( ) ( ) ( ) ( ) | ( W D P W B P W B P W P W B P W B P + = = Ex- Bayes) P(A3|bl)= ) 1 ( ) 1 | ( ) 2 ( ) 2 | ( ) 3 ( ) 3 | ( ) 3 ( ) 3 | ( A P A bl P A P A bl P A P A bl P A P A bl P + + -Independent if P(A|B)=P(A), or P(AandB)=P(A)P(B) -Expected=E(x)= = allN n n x x p x ) ( μ -Variance shortcut V(X)= 2 2 2 )] ( [ ) ( X E X E - = -Binomial b(x; n,p)= x n x p p x n x n - - - ) 1 ( )! ( ! ! where n=number of trials and p=probability Ex) P(error)=.005, 400 pages, P(one page with error)= b(1;400,.005) Ex) 300 parts, pick random 20, 10% are bad, the P(1 bad)= b(1;20,0.10) -Negative binomial nb=(x;r,p)= r r p p r x r x ) 1 ( )! 1 ( ! )! 1 ( - -
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Unformatted text preview: -+ where r=number of successes Ex) p(accept)=.2 , r=need 5, the P(15 need to be asked) = nb(10,5,0.2)-Hypergeometric h(x;n,M,N)= N n M N x n M x C C C , , ,--N=population, M=successes in pop, n=sample selected Ex) section 1=20, section 2= 30, 15 are graded, P(10 from section 2)= h(10;15,30,50) -Poisson ! ) ( ) ; ( x e x p x λ-= where λ=rate/time. Can estimate λ=E(X)=V(X) Ex) when you are doing at most x do a summation of all numbers up to x Ex) mean 3hits/min, P(10hits in 5 min)?, get 3h/m= 15h/5m, …p(10, 15)-Poisson Process ! ) ( ) ( x t e t P x t x α-= where λ=αt Pmf E(X) V(X) Binomial np np(1-p) Negative Binomial p p r ) 1 (-2 ) 1 ( p p r-Hypergeometric N nM ) 1 ( ) )( ( 2---N N n N M N nM Poisson λ λ...
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