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The convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear combinations of random variables. The operation here is a special case of convolution in the ...
This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations). [1]
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 ...
t. e. In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
Wald's equation. In probability theory, Wald's equation, Wald's identity[1] or Wald's lemma[2] is an important identity that simplifies the calculation of the expected value of the sum of a random number of random quantities. In its simplest form, it relates the expectation of a sum of randomly many finite-mean, independent and identically ...
The cumulative distribution function of a real-valued random variable is the function given by [2]: p. 77. (Eq.1) where the right-hand side represents the probability that the random variable takes on a value less than or equal to . The probability that lies in the semi-closed interval , where , is therefore [2]: p. 84.
Rademacher. In probability theory and statistics, the Rademacher distribution (which is named after Hans Rademacher) is a discrete probability distribution where a random variate X has a 50% chance of being +1 and a 50% chance of being −1. [1] A series (that is, a sum) of Rademacher distributed variables can be regarded as a simple ...
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are often employed for their succinct description of the sequence of probabilities Pr (X = i) in the ...