Midterm 1 - I.05 method for kth%ile Returns item place in...

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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(larger-smaller). 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]=n-p V(x)=np(1-p) 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
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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 wear-out Has lack of memory E(X) =  , V(x)= e.g. X= distance until first crack, and need to find probability of no cracks in 10-mile 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]=c µ 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=(i-0.5)/n E(A-B) = E(A)-E(B) V(A+-B) = V(A)+V(B) e.g. A:n(stuff) B:n(stuff) C:n(stuff) D=A-B-C 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 x-bar is sampling mean,
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Then   is n(0, 1) as n-> infinity Type I error:  Rejecting H when it is true.  Type II error:  Failing to reject H 0  when it is false. =P(type I error) = P(reject H α 0  when H 0  is true) P-value  is smallest level of significance that would lead to rejection of H 0 .
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