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ZB" z" ;,&2zInference GoalpTo use sample data to estimate population parameters. Example: use to estimate m But, would like accuracy of estimate. If unbiased, accuracy is just SD of , estimated by P6 &:RC OSampling Distribution of Approx Normal (CLT) Expected Value of is m (the population mean) SD of is is s/ called standard error (s is the population SD and n is the sample size) Usually, m and s must be estimated from the sample, using and s.-  0 $$7((,Conditional ProbabilityWP(A|B) = P(A and B)/P(B) where A and B are events (i.e. sets of sample space outcomes) XZXVUniform DistributionstDiscrete P(X=x) = 1/n x=1,2,3,& ,n Mean = (n+1)/2 SD = Continuous for 0<x<c and 0 otherwise. Mean = c/2 SD = Z(^" " (w 6     Model LinksWaiting time for kth success - neg. bin. Waiting time for rth event - gamma Waiting time for first success - geom. Waiting time for first event - exponential Number of events during time - Poisson ---------------- Time between successive events - expb)#'+ '$ t /3 LShape of Gamma familylParameters a, b a = 1 -> exponential a large -> normal a moderate -> right skew b contracts or expands scale. Mean = ab SD = b Determining reasonable a, b (Use Mean&SD)Z e t%Q"The bootstrap - bare bones:A statistic t(x1,x2,& ,xn) estimates parameter q Need: SD of t(), since it is precision of estimate. Method: Re-Sample (x1,x2,& ,xn) many times and compute t() each resample. Then compute SD of resample values of t(). Result - an estimate of the precision of t() as an estimate of q.  7 $$((,,004488<  j& Overview of Ch 1-6 / ! 1 ( aAxobtvcaa l  C PBoP   l  C Co  r  6A *??@ P %  *H  0޽h ? 33___PPT10u.1sh+D=' = @B + xVOoEvBt @*'N6"qv*jCJ)xzYB qC8q afgD:Eʳz7f潙pބ` gm`tOIe ~sl9^#2&Rzh7JԾ6)@ gLuІű _jNWL6 }%,g骙U 7V5 "jf/;W YPk5}%y8CY?3Y6}W9"Lq^K#quRpqF l۷ˠ*辣$|BLPڃ0įiΨc׻?/`zCש0'koX