Prib. of events. et PCA)Prob. of complex events. eg.P(AMB)Random Variable.CategoricalX is the color of the studentthart enters the door nextX=Red} {X=Blue}Quantitatives Generic Distribution.Special Distribution.Generic Distribution.X023P(X=1)020.3 0.1 0.4Pcx<1) =Area (ΣΧΕΣ)Area (S)0.240.3= 0.5Similar to categorical variable da proud of•everes,Special Distribution.discrete.离散Binomial distribution{Geometric distributionContinuous is normal连续 1 uniformeg 1.HHHHTHHHTHTHHITHHT. VTVITHHT33 coin toss.THT ✓TTH Vexactly I head.Tㅜ.ㅜㅜPL1 head)=3个total#ofoutomesBinomial Settings (Remember!!!)1). fixed number of trials n2) only.Sucess2 outromes each trialor failure.define yourself.3). fixed sucess prob. P.4). independent trials.X represent the number of sucess in n.4. trialsBinomial formula. غاBinomial. PDF...PDFnKn-kP(XK)Keg2: P(X=2) = 50.2 (1-0.2)3て271is(2)=(5 = 21/05/201nK=2!(5-2)!n=n!k!(n-k)!Binomial CDF.P(x≤k) = P(X=0) + P(X=1) + ··· +P(X=K)in, 5 prob. of successX ~ Binom (n, PR.V服从二项分布for each trial.max trialsE(X) = Mx = np↑expectedValue↓mean ofXStd(x) = 6x = Jupcr-p>↑std. of X.当P>0.5.x symmetric当up10, nc1-p)210时. X→Binom > Normalskew to the righ0当P→1時・且M(1-p)<10畔、右裁断.Skew to the left(NX~ Geometric C几何分布X是多次实验,第一次成功的序数。Mit SP(X=k)=(1-p)*1 P