Introduction to ProbabilityDeveloped from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional |
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approximation Assume average balls Bayes Bernoulli trials Beta distribution Bin(n,p Binomial birthday cards Chapter choose compute conditional distribution conditional expectation conditional PMF conditional probability constant continuous r.v. covariance defined diāµerent discrete r.v. event example expected number expected value Expo Exponential Figure Find the CDF Find the expected Find the joint Find the probability finite flip Fred function Gamma Gamma distribution Geometric given gives Hint Hypergeometric independent indicator r.v.s integral interval intuitively joint distribution joint PDF lands Heads large numbers law of total linearity LOTP LOTUS marginal distribution marginal PDF Markov chain mean and variance median Metropolis-Hastings algorithm nonnegative Normal distribution order statistics outcomes parameters pebbles Poisson process problem process with rate random variable randomly result sample mean sample space says Show simulation standard Normal stationary distribution statistics success Suppose symmetry Theorem tosses transition matrix Uniform Var(X