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Unformatted text preview: I+.05 method: for kth %ile. Returns item place in array of ordered set. K as integer. N+1 method: . K in decimal form. For interpolators (e.g. 3.5), ipart + fpart(largersmaller). Sample mean is just average Sample variance PDFs: P(a<x<b) = 1) F(x) >= 0 i.e. 2) CDF: F(x) = P(X<x) = . Shows amount of probability to that point. f(x) = some PDF µ=E[x]= Normal Distribution: X:n(µ, σ 2 ) > P(Z>z)=P(Z<z) PMFs: 1) F(x) >= 0 for all x 2) =1 Binomial distribution (discrete): Deals with some # of trials with one of two outcomes (success or failure in general) E[x]=np V(x)=np(1p) CDF of: Poisson Distribution (discrete): P(X=x)= X:p(x, ), and x is # of some event in some time/distance λ Poisson is for some defined interval with events occurring at random 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. Exponential Distribution (continuous): Timed, so not binomial/poisson Time between successive events of a Poisson process PDF: for Good for slow wearout Has lack of memory E(X) = , V(x)= e.g. X= distance until first crack, and need to find probability of no cracks in 10mile stretch P(X> 10)= If there are a # of cracks in 10 miles, use Poisson Joint PDFs: F(x,y)> P(a< x<b, c< Y< d) = Let Y = x+ c E[Y]= E(X+ c), E[x]= µ = E[x]+ E[c]> µ+c V(Y)= V(X)+ V(c)= V(X)= σ 2 Y=cx 1 , E[Y]=cE[x]=cµ V(Y)=c 2 V(X) = c 2 σ 2 Y=c 1 x 1 +c 2 x 2 +…c n x n E(Y)=c 1 µ 1 +c 2 µ 2 +…+c n µ n V(Y)=c 1 2 σ 1 2 +c 2 2 σ 2 2 … Normal Prob. Plots 1) Rank data in ascending order 2) Plot each pt with i.5 method (P=(i0.5)/n E(AB) = E(A)E(B) V(A+B) = V(A)+V(B) e.g. A:n(stuff) B:n(stuff) C:n(stuff) D=ABC E(D) = µ A +µ B +µ C V(D) = σ A 2 + σ B 2 + σ C 2 Central Limit Theorem: If underlying population is unknown, X1,x2…xn R.S. (mu, sigma squared), and if xbar is sampling mean, Then is n(0, 1) as n> infinity Type I error: Rejecting H 0 when it is true. Type II error: Failing to reject H when it is false....
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This note was uploaded on 09/17/2008 for the course IEE 380 taught by Professor Andersonrowland during the Spring '06 term at ASU.
 Spring '06
 andersonrowland

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