By Rick Durrett
This e-book is an creation to likelihood idea protecting legislation of enormous numbers, significant restrict theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian movement. it's a complete therapy focusing on the consequences which are the main important for functions. Its philosophy is that how to study likelihood is to determine it in motion, so there are 2 hundred examples and 450 problems.
"This ebook can be an exceptional source. numerous fascinating and urban examples are provided through the textbook, on the way to support newcomers receive a greater realizing of the basics of likelihood theory."
Ramesh Garimella, Computing Reviews
"The most sensible function of the booklet is its collection of examples. the writer has performed a unprecedented task in exhibiting now not easily what the provided theorems can be utilized for, but additionally what they can not be used for."
Miklos Bona, SIGACT News
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Extra info for Probability: Theory and Examples (4th Edition)
The potential payoff associated with the “×” option is mind-numbingly large, albeit highly unlikely. 7 × 10113), and we tend to appreciate this in terms of its intrinsic worth, or utility, rather than its actual value. So, we compare the expected utilities of the two options, rather than the expected payoffs. To simplify the discussion we use the common (base 10) logarithm of a payoff as a measure of its utility. (The common logarithm of a positive real number is the power to which 10 must be raised to yield the number.
Up or down? If, say, 1,000 such tacks are tossed and 160 land point up, we could invoke Bernoulli’s law of large numbers and assume the true probability is approximately equal to the experimental probability of 160/1000 = 4/25 or 16 percent. A more reliable estimate could be achieved by tossing a larger number of tacks and recording the results. In practice empirical probabilities are used as estimates of true probabilities because the true (theoretical) probabilities are not generally accessible.
Doing the Right Thing 43 is the case for all casino games; otherwise, the casino would lose money and go out of business. For Keno the house advantage can be as large as 27 percent, and for slot machines it varies between 4 percent and 8 percent.
Probability: Theory and Examples (4th Edition) by Rick Durrett