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As a discrete probability space, the probability of any particular lottery outcome is atomic, meaning it is greater than zero. Therefore, the probability of any event is the sum of probabilities of the outcomes of the event. This makes it easy to calculate quantities of interest from information theory.
In expected utility theory, a lottery is a discrete distribution of probability on a set of states of nature. The elements of a lottery correspond to the probabilities that each of the states of nature will occur, (e.g. Rain: 0.70, No Rain: 0.30). [ 1 ]
The St. Petersburg paradox or St. Petersburg lottery [1] is a paradox involving the game of flipping a coin where the expected payoff of the lottery game is infinite but nevertheless seems to be worth only a very small amount to the participants. The St. Petersburg paradox is a situation where a naïve decision criterion that takes only the ...
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
The theory of subjective expected utility combines two concepts: first, a personal utility function, and second, a personal probability distribution (usually based on Bayesian probability theory). This theoretical model has been known for its clear and elegant structure and its considered by some researchers to be "the most brilliant axiomatic ...
The lottery ′ is, in effect, a lottery in which the best outcome is won with probability (), and the worst outcome otherwise. Hence, if u ( M ) > u ( L ) {\displaystyle u(M)>u(L)} , a rational decision maker would prefer the lottery M {\displaystyle M} over the lottery L {\displaystyle L} , because it gives him a larger chance to win the best ...
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The concept is named after Siméon Denis Poisson.