PROBABILITY II STAT 395
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This 1 page Study Guide was uploaded by Providenci Mosciski Sr. on Wednesday September 9, 2015. The Study Guide belongs to STAT 395 at University of Washington taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/192510/stat-395-university-of-washington in Statistics at University of Washington.
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Date Created: 09/09/15
MATHSTAT 395 Midterm1 Winter 2009 Feb 6 2009 Useful facts 1 Permutations and combinations There are n Lli 1234 n permutations of 71 objects There are Z nlkln 7 ways of choosing a given k objects from n 2 Joint and conditional probabilities If C and D are any events PCUD PC The conditional probability of C given D is PC l D C and D are independent if PC D PCPD PD 7 mama gt 7 PC DPD 3 Laws and theorems Suppose E1 Ek is a partition of 9 That is Ei Ej is empty and E1 UEZU UEk Q The law of total probability states that PD 21PDQE Ef pw Ej PE Bayes7 Theorem states that PE D PD PEPD 4 Random variables and distributions discrete mass continuous density Probability massdensity function pmf PX z pXm pdf fXm Cumulative dist func CDF PX z Eygmpxty foo fXydy Joint massdensity func of XY pxy y PX zY y fxyy Marginal massdensity of X pXz ZyPX zY y fXm 5700 fxyz ydy Independence of X and Y pxyx y PX zPY y fxyz y fXzfyy Expectation EX 2mm PX z or 50 zfXmdz and EgX Emgw PX z or 50 gzfXzdm provided the sumintegral converges Variance varX EX 7 EX2 EX2 7 EX2 5 Standard distributions pmf or pdf mean variance a Binomial BOW PX k Z 2 7W mp 71290719 index n parameter p k 012 n b Geometric C29 PX k 290719 119 1 7pp2 parameter p k 1 2 3 4 k 7 1 c Neg Binomial NegBrp M 7 k 7 1 pm 729 rp rlt17pgtp2 T 7 index r parameter p k 737 1r 2 d Poisson 7300i PX k exp7uukkl k 0 1 2 ii i e Uniform on 11 Uab fXm 1b 7 a a lt z lt b b a2 b 7 a212 f Normal N 02 X z 1 271172 ex 7 z 7 2 202 02 M v p M M g Exponential fXm exp7m 1 12 rate parameter 0 g z lt 00 g Gamma Ca fXm xu za l exp7mFa Oz a2 shape 04 rate 0 g z lt oo
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