RSH_10_Ch_2

2008 Prentice-Hall, Inc.Chapter 2Probability Concepts and Applications 2008 Prentice-Hall, Inc.2 2Chapter Outline2.1 Introduction2.2 Fundamental Concepts2.3 Mutuall !"clusi#e and Collecti#el !"$austi#e !#ents2.% &tatisticall Independent !#ents2.' &tatisticall (ependent !#ents2.) *e#isin+ Pro,a,ilities -it$ .aes/ 0$eorem2.1 Furt$er Pro,a,ilit *e#isions 2008 Prentice-Hall, Inc.2 3Chapter Outline2.8 *andom 2aria,les2.3Pro,a,ilit (istri,utions2.100$e .inomial (istri,ution2.110$e 4ormal (istri,ution2.120$e F (istri,ution2.13 0$e !"ponential (istri,ution2.1%0$e Poisson (istri,ution 2008 Prentice-Hall, Inc.2 %Introduction5i6e is uncertain, -e are not sure -$at t$e 6uture -ill ,rin+*is7 and pro,a,ilit is a part o6 our dail li#esProbabilityProbability is a numerical statement a,out t$e li7eli$ood t$at an e#ent -ill occur 2008 Prentice-Hall, Inc.2 'Fundamental Concepts1. 0$e pro,a,ilit, P, o6 an e#ent or state o6 nature occurrin+ is +reater t$an or e8ual to 0 and less t$an or e8ual to 1. 0$at is90 P :e#ent; 12. 0$e sum o6 t$e simple pro,a,ilities 6or all possi,le outcomes o6 an acti#it must e8ual 1 2008 Prentice-Hall, Inc.2 )Diversey Paint Example (emand 6or -$ite late" paint at (i#erse Paint and &uppl $as al-as ,een eit$er 0, 1, 2, 3, or % +allons per da?40I0@ (!M?4(!(4>M.!* %.33; A 0.0'0$ere is onl a 'J pro,a,ilit t$at F -ill e"ceed %.33 2008 Prentice-Hall, Inc.2 8%FThe F DistributionFi+ure 2.1' 2008 Prentice-Hall, Inc.2 8'The F DistributionFi+ure 2.1)F A %.330.0'F #alue 6or 0.0' pro,a,ilit -it$ ' and ) de+rees o6 6reedom 2008 Prentice-Hall, Inc.2 8)The Exponential Distribution0$e exponential distributionexponential distribution :also called t$e ne$ative exponential distributionne$ative exponential distribution; is a continuous distri,ution o6ten used in 8ueuin+ models to descri,e t$e time re8uired to ser#ice a customerxe X f= ) (-$ereX A random #aria,le :ser#ice times; A a#era+e num,er o6 units t$e ser#ice 6acilit can $andle in a speci6ic period o6 timee A 2.118 :t$e ,ase o6 natural lo+arit$ms; 2008 Prentice-Hall, Inc.2 81The Exponential Distributiontime ser#ice ?#era+e1#alue !"pected = =212ariance=f:X;XFi+ure 2.11 2008 Prentice-Hall, Inc.2 88The Poisson Distribution0$e PoissonPoisson distributiondistribution is a discretediscrete distri,ution t$at is o6ten used in 8ueuin+ models to descri,e arri#al rates o#er time!) (XeX Px =-$ereP:X; A pro,a,ilit o6 e"actl H arri#als or occurrences A a#era+e num,er o6 arri#als per unit o6 time :t$e mean arri#al rate;e A 2.118, t$e ,ase o6 natural lo+arit$msX A speci6ic #alue :0, 1, 2, 3, and so on; o6 t$e random #aria,le 2008 Prentice-Hall, Inc.2 83The Poisson Distribution0$e mean and #ariance o6 t$e distri,ution are ,ot$ !"pected #alue A 2ariance A 0.3 0.2 0.1 0 K K K K K K K K K K0 1 2 3 % ' ) 1 8P:X;XFi+ure 2.18