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MATH 2P82 MATHEMATICAL STATISTICS (Lecture Notes)

MATH 2P82 MATHEMATICAL STATISTICS (Lecture Notes) c Jan Vrbik23 Contents1 PROBABILITY REVIEW7 Basic 7 binomial 7 Multinomial 7 Random Experiments (Basic Definitions).. 7 Sample 8 Set 8 Boolean 8 Probability of 8 Probability 9 Important 9 Probability 9 Product 9 Conditional 9 Total-probability 10 Discrete Random 10 Bivariate (joint) 11 Conditional 11 Multivariate 11 Expected Value of a 11 Expected values related 12 Moments (univariate).. 12 Moments (bivariate or joint ).

(number of combinations). This will also be called the binomial coeffi-cient. If we can duplicate (any number of times), and count the arrangements: nr Binomial expansion (x+y) n= Xn i=0 ³n i ´ x−iyi Multinomial expansion (x+y+z)n X i,j,k≥0 i+j+k=n µ n i,j,k ¶ xiyjzk (x+y+z+w)n= X i,j,k,c≥0 i+j+k+c=n µ n i,j,k,c ¶ xiyjzkwc etc ...

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