E7_Lecture22_F08_Probability

# E7_Lecture22_F08_Probability - 1 E7: INTRODUCTION TO...

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5 Probability - Sample space, outcome, event Sample space, outcome, event xperiment: rowing a pair of dice (one d nd one lue Experiment: throwing a pair of dice (one red and one blue) the sample space has 36 outcomes: S = he event f obtaining the number The event L of obtaining the number 7 is { } ( , ),( , ),( , ),( , ),( 12345 65432 ,) , ( ) 1 6 , L = E7 L20 L occurs if any of the outcomes in L occurs. Probability number between 0 and 1 inclusive that indicates 6 A number between 0 and 1, inclusive, that indicates how likely an event is to occur . – An event with probability of 0 is a null event. – An event with probability of 1 is a certain event. • Probability of event A is denoted as P(A) . • The closer P(A) to 1, the more likely is A to happen. E7 L20 Probability number between 0 and 1 inclusive that indicates 7 A number between 0 and 1, inclusive, that indicates how likely an event is to occur . • An event with probability of 0 is a null event. – a man gets pregnant – a woman dies of prostate cancer p n event with probability of 1 is a ertain event. An event with probability of 1 is a certain event. – the sun will set tonight – a person eventually dies E7 L20 Assigning Probability Assigning Probability - frequentist frequentist approach approach 8 • An experiment is repeated n times under essentially identical conditions • if the event A occurs m times, then as n grows large () m PA n E7 L20
9 Dice example xperiment: rowing of a ir ice once Experiment: throwing of a fair dice once S = 2,3,4,5,6 = { } 1,2,3,4,5,6 S P(S) = 1 P(1) = 1/6, P(3) =1/6, P(6) = 1/6 P(even number) = 3/6 = 1/2 E7 L20 P(odd number) = 3/6 = 1/2 Random numbers Random numbers – matlab simulation

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## This note was uploaded on 11/01/2009 for the course ENGLISH 7 taught by Professor Sengupta during the Spring '09 term at Berkeley.

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E7_Lecture22_F08_Probability - 1 E7: INTRODUCTION TO...

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