Transcription of MATH 2P82 MATHEMATICAL STATISTICS (Lecture Notes)
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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 ).. 12 Variance ofaX+bY+ 13 Moment generating 13 Main 13 Probability generating 13 Conditional expected 14 Common discrete 14 Negative 15 Multivariate 15 Continuous Random 16 Univariate probability density function (pdf).. 16 Distribution 16 Bivariate (multivariate) 16 Marginal 16 Conditional 17 Mutual 17 Expected 17 Common Continuous 18 Transforming Random 192 Transforming Random Variables21 Univariate 21 Distribution-Function(F) 21 Probability-Density-Function(f) 23 Bivariate 24 Distribution-Function 24 Pdf (Shortcut) 253 Random Sampling31 Sample 31 Central Limit 31 Sample 32 Sampling fromN( , ).
6! 3!2!1! def.= µ 6 3,2,1 ¶ or N! n 1!n 2!n 3!.....nk! def.= µ N n 1,n 2,n 3,....,nk ¶ in general, where N= Pk i=1 niwhich is the total word length (multinomial coef-ficient). Selecting rout of nobjects (without duplication), counting all possible arrange-ments: n×(n−1) ×(n−2)×....×(n−r+1)= n! (n−r)! def.= Pn r (number of ...
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