A First Course in ProbabilityFor upper level or undergraduate/graduate level introduction to probability for math, science, engineering, and business students with a background in elementary calculus. This market-leading introduction to probability features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. The outstanding problem sets and intuitive explanations are hallmark features of this market leading text. |
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Page 62
... denote the event that the midtown temperature in Los Angeles is 70 ° F , and let B denote the event that the midtown temperature in New York is 70 ° F . Also , let C denote the event that the maximum of the midtown temperatures in New ...
... denote the event that the midtown temperature in Los Angeles is 70 ° F , and let B denote the event that the midtown temperature in New York is 70 ° F . Also , let C denote the event that the maximum of the midtown temperatures in New ...
Page 84
... denote the event that the sum of the dice is 6 and F denote the event that the first die equals 4. Then whereas P ( E1F ) = P ( { ( 4,2 ) } ) 1 = 36 5 P ( E1 ) P ( F ) = ( 3 % ) ( b ) = 216 36 Hence E , and F are not independent ...
... denote the event that the sum of the dice is 6 and F denote the event that the first die equals 4. Then whereas P ( E1F ) = P ( { ( 4,2 ) } ) 1 = 36 5 P ( E1 ) P ( F ) = ( 3 % ) ( b ) = 216 36 Hence E , and F are not independent ...
Page 483
... denote the event that the life of the battery is greater than 10,000 × i miles . ( a ) P ( L2 | L1 ) = P ( L1L1⁄2 ) ... event that the transferred ball is white , and let W be the event that a white ball is drawn from urn B. Then P ( TW ) ...
... denote the event that the life of the battery is greater than 10,000 × i miles . ( a ) P ( L2 | L1 ) = P ( L1L1⁄2 ) ... event that the transferred ball is white , and let W be the event that a white ball is drawn from urn B. Then P ( TW ) ...
Contents
AXIOMS OF PROBABILITY | 24 |
CONDITIONAL PROBABILITY AND INDEPENDENCE | 64 |
RANDOM VARIABLES | 122 |
Copyright | |
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approximately assume binomial random variable black balls cards central limit theorem Chebyshev's inequality components compute conditional probability Consider continuous random variable Cov(X defined denote the event denote the number desired probability dice discrete random variable distribution function distribution with parameters equal Equation Example expected number expected value exponential random variable Find the probability flips follows function F Hence HINT independent trials inequality joint density function large numbers least Let X denote moment generating function nonnegative normal random variable normally distributed obtain occur P(EF P₁ P₂ pair percent permutation player Poisson random variable preceding prob probability density function probability mass function problem Proposition random number random vari randomly chosen result sample space sequence Show simulate Solution Let Suppose uniformly distributed Var(X variable with mean variable with parameters white balls wins X₁ Y₁ Y₂ Σ Σ