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The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. If the random variable is denoted by X {\displaystyle X} , then the mean is also known as the expected value of X {\displaystyle X} (denoted E ( X ) {\displaystyle E(X)} ).
The value of the normal density is practically zero when the value lies more than a few standard deviations away from the mean (e.g., a spread of three standard deviations covers all but 0.27% of the total distribution).
Discrete probability distribution: for many random variables with finitely or countably infinitely many values. Probability mass function (pmf): function that gives the probability that a discrete random variable is equal to some value. Frequency distribution: a table that displays the frequency of various outcomes in a sample.
The mean of gamma distribution is given by the product of its shape and scale parameters: ... The median for this distribution is the value ...
the arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded. Interquartile mean a truncated mean based on data within the interquartile range. Midrange the arithmetic mean of the maximum and minimum values of a data set. Midhinge the arithmetic mean of the first and third ...
Mean for beta distribution for 0 ≤ α ≤ 5 and 0 ≤ β ≤ 5. The expected value (mean) (μ) of a beta distribution random variable X with two parameters α and β is a function of only the ratio β/α of these parameters: [1]
The log-normal distribution is the maximum entropy probability distribution for a random variate X —for which the mean and variance of ln(X) are specified. [ 5 ] Definitions
The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables, each of which clusters around a mean value. Definitions