Lecture 27 Roberto Horowitz. Yovisto Academic Video Search. "Lecture 27" Speaker: "Roberto HOROWITZ" Berkeley - University of California Speaker: "Roberto HOROWITZ" problemi Hall Monthy probabilities Estimates hal monthy tch swj Pno red le6 1e4 1e2 simulation matlab picking Ball slide previous from continues cked Balls function simulation matlab picking Ball slide next simulation matlab picking Ball Labels probabilities some calculate lets question this answer balls red two probability What picking Ball balls red two probability What picking Ball balls red two probability What picking Ball white two red jar one balls are There picking Ball has event each exclusive mutually are events obtaining probability glg blue one dice pair throwing Experiment Example blue one dice pair throwing Experiment blue one dice pair throwing Experiment Example twice count don AQB AUB exclusive mutually are occur both means Union Law occur both means Union Law xpl are both outcomes probability assigning approach Axiomatic probability assigning approach Axiomatic both are that outcomes denoted union events two Union outcomes possible out of1 probability jig blue one dice pair throwing Experiment independence Example blue one dice pair throwing Experiment independence Example LZO blue outcomes has space sample Gnd ofg pair throwing Experiment dice fair two Throwing Elf LiI exclusive mutually are Events once dice throwing Experiment events two Intersection Example independent exclusive mutually are both outcomes probability assigning approach Axiomatic both outcomes probability assigning approach Axiomatic space sample OSP eventA probability assigning approach Axiomatic events two Complement Intersection Union events two Complement Intersection Union Complement Intersection Union bar length edges stc outcome each probability plotting matlab vector elements between values number counts edges commands histogram matlab value that oftimes vector elements between values number counts edges function hista commands histogram matlab times dice fair Throw simulation matlab Sum enough large sum zeros BIIS leo land test function rand Matlab simulation matlab numbers Random XSQ between number distributed uniformly generates function rand Matlab simulation matlab numbers Random between number distributed uniformly generates function rand Matlab simulation matlab numbers Random LZFA once dice throwing Experiment example Dice grows then occurs event conditions identical essentially under times repeated experiment approach frequentist Probability Assigning occur event how indicates that inclusive between number Probability any occurs number obtaining outcomes has sample blue one dice pair throwing Experiment event outcome space Sample Probability ill outcomes has sample blue one dice pair throwing Experiment event outcome space Sample Probability blue one dice pair throwing Experiment event outcome space Sample Probability odd dots number even observing event once dice throwing Experiment events Probability dots number even observing event once dice throwing Experiment events Probability once dice throwing Experiment events Probability subsets Are Events space sample elements Outcomes IEIE once dice throwing Experiment events Probability USA Califomia Stanford Way Abbott Nathan send ons http visit license this copy view License Alike Commons Creative under licensed work This Packard Horowitz Copyright histograms processes random model rand Using probability concepts Basic Outline Lecture ENGINEERS AND SCIENTISTS FOR PROGRAMMING COMPUTER INTRODUCTION once dice throwing experiment outcomes possible Space Sample chance depends outcome whose situation Experiment concepts some Probability