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Prob Theory

by: Carmen Mayer

Prob Theory STA 131A

Carmen Mayer
GPA 3.69

Debashis Paul

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Debashis Paul
Class Notes
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This 2 page Class Notes was uploaded by Carmen Mayer on Tuesday September 8, 2015. The Class Notes belongs to STA 131A at University of California - Davis taught by Debashis Paul in Fall. Since its upload, it has received 72 views. For similar materials see /class/191912/sta-131a-university-of-california-davis in Statistics at University of California - Davis.


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Date Created: 09/08/15
Spring 2009 Statistics 131A Handout 4 Some important discrete probability distributions Here are some facts about some discrete probability distributions 1 Binomialnp Probability mass function ltZgtpk0iz k k0L2Hn ZXXnnhMXnM1pl 2 Negative Binomialr7 p Probability mass function k 7 1 7 k7 pltkgtPltXkgt 7671190719 km EX VarX Special case r 1 Geometricp 3 Poisson Probability mass function Ak pas PltX k erg kQLZm EQ ampW k 4 Hypergeornet1quoticN7 m7 n Probability mass function kam 19kPXkW7 k01m1nmn 71 M i varltXgt Wi i 17 l Spring 2009 Statistics 131A Handout 1 Some important combinatorial objects 1 E0 00 4 CT CT Factorial notation For a positive integer 7 we use 7 to denote the product rgtltr71 gtlt gtlt2gtlt1 We alsode ne0l1 Permutations The number of ways of arranging n distinct objects in r ordered positions is given by P n 1 1 1 2 7ngtlt n7 gtltgtltnir r 7 7 7 7 7 7 Binomial coe icients The number of ways of selecting 7 objects from a collec tion of n distinct objects n n r 07 7n 7 ln 7 r Binomial theorem n 7quot k Lek z n z lt a Z y k0 Multinomial coe icients The number of ways of dividing n distinct objects into 7 groups of respective sizes 71177177 with m 2 0 for all i 17 7quot and 2171 nl n7 is given by n 7 n 71171277 T nlln2ln Number of integer solutions For any positive integer n7 number of solutions of the equation 12r71 where 1 7x7 are positive integers is given by lf instead the as are only non negative7 then the number of integer solutions equals


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