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Probability theory. In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while ...
The standard uniform distribution is a special case of the beta distribution, with parameters (1,1). The sum of two independent uniform distributions U 1 (a,b)+U 2 (c,d) yields a trapezoidal distribution, symmetric about its mean, on the support [a+c,b+d]. The plateau has width equals to the absolute different of the width of U 1 and U 2. The ...
Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
In probability theory and statistics, Student's t distribution (or simply the t distribution) is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, has heavier tails and the amount of probability mass in the tails is controlled by the ...
Normality test. In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. More precisely, the tests are a form of model selection, and can be interpreted several ways, depending on one's ...
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
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The characteristic function. of the sum of two independent random variables X and Y is just the product of the two separate characteristic functions: of X and Y. The characteristic function of the normal distribution with expected value μ and variance σ 2 is. {\displaystyle \varphi (t)=\exp \left (it\mu - {\sigma ^ {2}t^ {2} \over 2}\right).} So.