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This process can be generalized to a group of n people, where p(n) is the probability of at least two of the n people sharing a birthday. It is easier to first calculate the probability p (n) that all n birthdays are different. According to the pigeonhole principle, p (n) is zero when n > 365. When n ≤ 365:
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those ...
Pre-test probability and post-test probability (alternatively spelled pretest and posttest probability) are the probabilities of the presence of a condition (such as a disease) before and after a diagnostic test, respectively. Post-test probability, in turn, can be positive or negative, depending on whether the test falls out as a positive test ...
In probability theory and statistics, the Weibull distribution / ˈwaɪbʊl / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The arithmetic mean (or simply mean or average) of a list of numbers, is the sum of all of the numbers divided by their count. Similarly, the mean of a sample , usually denoted by , is the sum of the sampled values divided by the number of items in the sample. For example, the arithmetic mean of five values: 4, 36, 45, 50, 75 is:
Weighted arithmetic mean. The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also ...
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. [1] From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a ...
A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often represented in notation by is the set of all possible outcomes of a random phenomenon being observed. The sample space may be any set: a set of real numbers, a set of descriptive labels, a set of vectors ...