Books written by Jeffrey S. Rosenthal

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  Probability and Statistics: The Science of Uncertainty

  Theorem 3.4.9 Let X be any random variable with its first k moments finite. Then cX (0) = 1, o;( (0) = iE(X), egg (0) = i2E(X2) = —E(X2), etc. In general, cgc)(0) = ikE(Xk), where i = s/ —1, and where cg?) is the kth derivative of cX.

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  Probability and Statistics: The Science of Uncertainty

  X2 OŹx n2 102 ° 1x ( a ) Prove that fx ( x ) = pfix ( 2 ) + ( 1 – p ) fax ( 2 ) . ( b ) Establish that px = puix + ( 1 – p ) Max where fix is the mean of X on IIį . ( c ) Establish that ož = poix + ( 1 - p ) oźx + p ( 1 – p ) ( 41x ...

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  Knock on Wood: Luck, Chance, and the Meaning of Everything

  In Knock on Wood, Rosenthal, with great humour and irreverence, divines the world of luck, fate, and chance, putting his considerable scientific acumen to the test in deducing whether luck is real or the mere stuff of superstition.

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  Struck by Lightning: The Curious World of Probabilities

  From terrorist attacks to big money jackpots, Struck by Lightning deconstructs the odds and oddities of chance, examining both the relevant and irreverent role of randomness in our everyday lives.

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  A First Look at Rigorous Probability Theory

  This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.