MATH 2P82 MATHEMATICAL STATISTICS (Lecture Notes)

← Back to document page

MATH 2P82MATHEMATICAL STATISTICS (Lecture Notes) c Jan Vrbik23Contents1 PROBABILITY REVIEW7Basic 7Binomial 7Multinomial 7Random Experiments (Basic Definitions).............. 7Sample 8Set 8Boolean 8Probability of 8Probability 9Important 9Probability 9Product 9Conditional 9Total-probability 10Discrete Random 10Bivariate (joint) 11Conditional 11Multivariate 11Expected Value of a 11Expected values related 12Moments (univariate)........................ 12Moments (bivariate or joint )................... 12Variance ofaX+bY+ 13Moment generating 13Main 13Probability generating 13Conditional expected 14Common discrete 14Negative 15Multivariate 15Continuous Random 16Univariate probability density function (pdf)......... 16Distribution 16Bivariate (multivariate) 16Marginal 16Conditional 17Mutual 17Expected 17Common Continuous 18Transforming Random 192 Transforming Random Variables21Univariate 21Distribution-Function(F) 21Probability-Density-Function(f) 23Bivariate 24Distribution-Function 24Pdf (Shortcut) 253 Random Sampling31Sample 31Central Limit 31Sample 32Sampling fromN( , ).

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 permutations). Forget their final arrangement: Pn r r! = n! (n−r)!r! def.= Cn r (number of combinations). This will also be called the binomial coeffi-cient.

  Selecting