A First Course in Probability |
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Contents | 2 |
On the Distribution of Balls in Urns | 11 |
Axioms of Probability | 17 |
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A₁ approximation assume ball number ball selected binomial random variable black balls cent Chebyshev's inequality Compute the probability conditional probability Continuous Random Variables cumulative distribution function defined denote the event denote the number desired probability dice discrete random variable Distributed Random Variables distributed with parameters dx dy E[X₁ E₁ equal Equation Example 3a expected number fair coin Find the probability flips follows function f(x Hence independent random variables independent trials joint probability large numbers law of large Let X denote moment generating function n₁ normal random variable normally distributed obtain P(EF P₁ P₂ player Poisson random variable prob Probability and Independence probability density function probability mass function problem Proposition prove Random Variables Ch result sample space sequence Solution Suppose Theoretical Exercises uniformly distributed urn contains variable with parameters variance white balls wins X₁ Y₁