Final Review Sheet

Final Review Sheet - I+.05 method: ( - . ) * = i 0 5 n 100...

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Unformatted text preview: I+.05 method: ( - . ) * = i 0 5 n 100 k for kth %ile. Returns item place in array of ordered set. K as integer. N+1 method: + = kn 1 i . K in decimal form. For interpolators (e.g. 3.5), ipart + fpart(larger-smaller). Sample mean is just average Sample variance = = ( - )- s2 i 1n xi x 2n 1 PDFs (Probability Distribution Functions): P(a<x<b) = abfxdx 1) F(x) >= 0 i.e. = fx kx2 < < , for 0 x 2 0 elsewhere 2)- ( ) f x = 1 3) CDF (Cumulative Distribution Functions): 4) F(x) = P(X<x) = - xfudu . Shows amount of probability to that point. 5) f(x) = some PDF 6) =E[x]=- xfxdx 7) = =-( - ) = -- 2 Vx x 2fxdx x2fxdx 2 8) Normal Distribution: 9) X:n(, 2 ) -> = - Z x 10) P(Z>z)=P(Z<-z) 11) 12) PMFs (Probability Mass Functions): 1) F(x) >= 0 for all x 2) ( ) f x =1 3) = = ( ) Ex xf x 4) = =- 2 VX Ex2 2 5) = =- = < , = F PX x xfx Fx 0 for x 1 Fx 18 for , . 1 x 3 etc 6) Binomial distribution (discrete): 7) Deals with some # of trials with one of two outcomes (success or failure in general) 8) : , = ( ) ( - ) - , = , , , X bn p fx xn px 1 p n x x 0 1 2 n 9) E[x]=n-p 10) V(x)=np(1-p) 11) CDF of: 0xpdf 12) Poisson Distribution (discrete): 13) P(X=x)=- ! e xx 14) X:p(x, ), and x is # of some event in some time/distance 15) Poisson is for some defined interval with events occurring at random 16) Assure events are random through the interval, and can be split into subintervals so that: 1) Probability of more than one count in a subinterval is 0 2) Prob. Of one count of subinterval is same for all, and proportional to length 3) Count in each sub. Is independent of other subintervals. 17) Exponential Distribution (continuous): 18) Timed, so not binomial/poisson 19) Time between successive events of a Poisson process 20) PDF: - e x for 0 x 21) Good for slow wear-out 22) Has lack of memory 23) E(X) = 1 , V(x)= 12 24) e.g. X=distance until first crack, and need to find probability of no cracks in 10-mile stretch 25) P(X>10)= - =- - 10 e x e x|10 26) If there are a # of cracks in 10 miles, use Poisson 27) 28) Joint PDFs: 29) F(x,y)->P(a<x<b, c<Y<d) = ( , ) abcdf x y dxdy 30) 31) Let Y = x+c 32) E[Y]=E(X+c), E[x]= 33) =E[x]+E[c]->+c 34) V(Y)=V(X)+V(c)=V(X)= 2 35) Y=cx 1 , E[Y]=cE[x]=c 36) V(Y)=c 2 V(X) = c 2 2 37) 38) Y=c 1 x 1 +c 2 x 2 +c n x n 39) E(Y)=c 1 1 +c 2 2 ++c n n 40) V(Y)=c 1 2 1 2 +c 2 2 2 2 41) 42) Normal Prob. Plots 1) Rank data in ascending order 2) Plot each pt with i-.5 method (P=(i-0.5)/n) 43) 44) E(A-B) = E(A)-E(B) 45) V(AB) = V(A)+V(B) 46) e.g. 47) A:n(stuff) 48) B:n(stuff) 49) C:n(stuff) 50) D=A-B-C 51) E(D) = A + B + C 52) V(D) = A 2 + B 2 + C 2 53) 54) Central Limit Theorem: 55) If underlying population is unknown, 56) X1,x2xn R.S. (mu, sigma squared), and if x-bar is sampling mean, 57) Then = - Z x n is n(0, 1) as n-> infinity 58) Type I error: Rejecting H 0 when it is true. Type II...
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This note was uploaded on 09/17/2008 for the course IEE 380 taught by Professor Anderson-rowland during the Spring '06 term at ASU.

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Final Review Sheet - I+.05 method: ( - . ) * = i 0 5 n 100...

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