Elements of Statistical Methods Probability (Ch 3) - Statistics

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Dice ExampleFor a pair of symmetric dice it seems reasonable to assume that all 36 outcomesin a proper roll of a pair of dice are equally likely.⎧(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)⎪⎨. . . . . .S =. . . . . .⎪⎩(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)⎫⎪⎬⎪⎭What is the chance of coming up with a 7 or 11?A = {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1),(6,5),(5,6)}with #(A) = 8 and thus P(A) = 8/36 = 2/9.Counting by full enumeration can become tedious and shortcuts are desirable.15
Combinatorial Counts40 patients in a preliminary drug trial are equally split between men and women.We randomly split these 40 patients so that half get the new drugwhile the other half get a look alike placebo.What is the chance that the “new drug” patients are equally split between genders?“randomly split” means: any group of 20 out of 40 is equally likely to be selected.P(A) =( 2010) (×20)10) = choose(20,10)ˆ2/choose(40,20)( 4020= dhyper(10,20,20,20) = 0.2476289See documentation in R on using choose and dhyper.( 40) (Enumerating 20 = 137,846,528,820 and 20 210)= 184,7562 cases is impractical.16
Page 1 and 2: Elements of Statistical MethodsProb
Page 3: Subjectivist Interpretation of Prob
Page 7 and 8: Collection of Events: Required Prop
Page 9 and 10: The Probability Measure PA probabil
Page 11 and 12: Countable Additivity =⇒ Finite Ad
Page 13 and 14: P(A ∪ B) = P(A) + P(B) − P(A
Page 15: Equally Likely OutcomesMany useful
Page 19 and 20: Rolling 5 Fair Dice (continued)c) W
Page 21 and 22: Matching or Adjacent BirthdaysWhat
Page 23 and 24: Conditional ProbabilityS● ● ●
Page 25 and 26: Two Headed/Tailed CoinsAsk Marilyn:
Page 27 and 28: Applying the Multiplication RuleP({
Page 29 and 30: P(D|T + )?Typically something is kn
Page 31 and 32: IndependenceThe concept of independ
Page 33 and 34: Implied IndependenceIf A and B are
Page 35 and 36: Postulated IndependenceIn practical
Page 37 and 38: Mutual Independence of a Collection
Page 39 and 40: Random Variables for Two Coin Tosse
Page 41 and 42: Induced Events and ProbabilitiesSup
Page 43 and 44: CDF for Single Coin Toss or Coin Sp
Page 45 and 46: 2 Fair Coin TossesFor two fair coin
Page 47 and 48: General CDF Properties1. 0 ≤ F(y)
Page 49: Independent Random VariablesA colle

Elements of Statistical Methods Probability (Ch 3) - Statistics

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