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In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.
That is, for each value of a in some set A, p(x;a) is a probability density function with respect to x. Given a probability density function w (meaning that w is nonnegative and integrates to 1), the function = (;) is again a probability density function for x. A similar integral can be written for the cumulative distribution function.
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Pages in category "Compound probability distributions" The following 23 pages are in this category, out of 23 total. This list may not reflect recent changes .
Probability is a measure of the likeliness that an event will occur. Probability is used to quantify an attitude of mind towards some proposition whose truth is not certain. The proposition of interest is usually of the form "A specific event will occur." The attitude of mind is of the form "How certain is it that the event will occur?"
In probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. Let E 1 {\displaystyle E_{1}} and E 2 {\displaystyle E_{2}} denote two mutually exclusive events which might occur on a given trial.
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]