Search results
Results From The WOW.Com Content Network
The first cumulant is κ 1 = K′(0) = μ and the other cumulants are zero, κ 2 = κ 3 = κ 4 = ⋅⋅⋅ = 0. The Bernoulli distributions, (number of successes in one trial with probability p of success). The cumulant generating function is K(t) = log(1 − p + pe t). The first cumulants are κ 1 = K '(0) = p and κ 2 = K′′(0) = p·(1 − p).
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 probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [3]
In this case, the expected utility of Lottery A is 14.4 (= .90(16) + .10(12)) and the expected utility of Lottery B is 14 (= .50(16) + .50(12)) [clarification needed], so the person would prefer Lottery A. Expected utility theory implies that the same utilities could be used to predict the person's behavior in all possible lotteries. If, for ...
Elementary events may occur with probabilities that are between zero and one (inclusively). In a discrete probability distribution whose sample space is finite, each elementary event is assigned a particular probability. In contrast, in a continuous distribution, individual elementary events must all have a probability of zero.
The balls into bins (or balanced allocations) problem is a classic problem in probability theory that has many applications in computer science.The problem involves m balls and n boxes (or "bins").
Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to 0.
When probability is expressed as a number between 0 and 1, the relationships between probability p and odds are as follows. Note that if probability is to be expressed as a percentage these probability values should be multiplied by 100%. " X in Y" means that the probability is p = X / Y. " X to Y in favor" means that the probability is p = X ...