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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,*,Defining Probabilities:Random Variables,Examples:,Out of 100 heart catheterization procedures performed at a local hospital each year,the probability that more than five of them will result in complications is,_,Drywall anchors are sold in packs of 50 at the local hardware store.The probability that no more than 3 will be defective is,_,In general,_,Discrete Random Variables,Example:,Look back at problem 3,page 46.Assume someone spends$75 to buy 3 envelopes.The sample space describing the presence of$10 bills(H)vs bills that are not$10(N)is:,_,The random variable associated with this situation,X,reflects the outcome of the choice and can take on the values:,_,Discrete Probability Distributions,The probability that there are no$10 in the group is,P,(,X=,0)=_,(recall results from last time),The,probability distribution,associated with the number of$10 bills is given by:,x,0,1,2,3,P,(,X=x,),Another Example,Example 3.3,pg 66,P,(,X=,0)=,_,Discrete Probability Distributions,The,discrete probability distribution function,(pdf),f,(,x,)=,P,(,X=x,),0,x,f,(,x,)=1,The,cumulative distribution,F,(,x,),F,(,x,)=,P,(,X x,)=,t x,f,(,t,),Probability Distributions,From our example,the probability that,no more than,2 of the envelopes contain$10 bills is,P,(,X,2,)=,F,(2)=_,The probability that,no fewer than,2 envelopes contain$10 bills is,P,(,X,2,)=1-,P,(,X,1,)=1-,F,(1)=_,Another View,The,probability histogram,Your Turn,The output from of the same type of circuit board from two assembly lines is mixed into one storage tray.In a tray of 10 circuit boards,6 are from line A and 4 from line B.If the inspector chooses 2 boards from the tray,show the probability distribution function associated with the selected boards being from line A.,x,P,(,x,),0,1,2,Continuous Probability Distributions,Examples:,The probability that the average daily temperature in Georgia during the month of August falls between 90 and 95 degrees is,_,The probability that a given part will fail before 1000 hours of use is,_,In general,_,Homework due dates,Friday,9/3pg.54-56,Wednesday,9/8 pg.72-74(both sets),(Check the web site on,Thursday,9/2,for an updated schedule.),
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