Stat 321 – Lecture 17RemindersQuiz 4 Lessons (for you)Lab 5 – Special Continuous DistributionsSlide 5Lecture 17 - Example 1Other CombinationsNew Rules…Slide 9Sample MeanCautionMoralStat 321 – Lecture 17Combining random variables (Ch. 5)RemindersLab 5 due todayHW 5 due tomorrowReview sheet/problems postedQuestion and Answer TuesdayLab 4 returned tomorrowHW 4 can be retrieved WednesdayHW 5 solutions posted Tuesday eveningExam 2 ThursdayQuiz 4 Lessons (for you)Take care in defining discrete random variable in wordsIf can use one of the common probability models, do so!Name of distribution and parameter values often enoughLab 5 – Special Continuous DistributionsmagnitudesFrequency4.84.23.63.02.41.81.20.69080706050403020100Mean 1.956StDev 0.6490N 614Histogram of magnitudesNormal NormalStandardize and use Table A.3 or use Minitab/applet• Comparisons over entire range• Easier to visually judge linear fit than pdf curveLab 5 – Special Continuous DistributionsmagnitudesFrequency4.84.23.63.02.41.81.29080706050403020100Histogram of magnitudesmagnitudesFrequency4.84.23.63.02.41.81.29080706050403020100Shape 9.921Scale 0.1971N 614Histogram of magnitudesGamma UniformInterval length/B-AIntegrate or geometryGammaStandardize and use Table A.4magnitudesFrequency8.47.26.04.83.62.41.20.09080706050403020100Mean 1.956N 614Histogram of magnitudesExponential ExponentialIntegrate f(x) or use F(x)magnitudesFrequency4.84.03.22.41.60.80.09080706050403020100Shape 3.107Scale 2.183N 614Histogram of magnitudesWeibull WeibullUse F(x)magnitudesFrequency4.84.23.63.02.41.81.29080706050403020100Loc 0.6196Scale 0.3180N 614Histogram of magnitudesLognormal LognormalTake log and use Table A.3Lecture 17 - Example 1Waiting at the bus stop…X1 is Uniform [0,5]E(X1) = 2.5 minV(X1) = (5-0)2/12 = 2 1/12 min2Y = X1 + X2Shape?Center?Spread?E(Y)= 50 5 xf(x)Other CombinationsY = X1 + X1Y = X1 + (2X1 -2)New Rules…Rules for Expected ValueE(X+Y) = E(X) + E(Y)Rules for VarianceV(X+Y) = V(X) + V(Y) IF X and Y are independentSample MeanCautionX1+…+X10 vs. 10X10 5 xf(x)MoralIt is often possible to find the distribution of combinations of random variables like sums and