Search results
Results from the WOW.Com Content Network
Clearly every well-distributed sequence is uniformly distributed, but the converse does not hold. The definition of well-distributed modulo 1 is analogous. Sequences equidistributed with respect to an arbitrary measure
If X has a standard uniform distribution, then by the inverse transform sampling method, Y = − λ −1 ln(X) has an exponential distribution with (rate) parameter λ. If X has a standard uniform distribution, then Y = X n has a beta distribution with parameters (1/n,1). As such, The Irwin–Hall distribution is the sum of n i.i.d. U(0,1 ...
The i.i.d. assumption is also used in the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution. [4] The i.i.d. assumption frequently arises in the context of sequences of random variables. Then, "independent and identically ...
Students of statistics and probability theory sometimes develop misconceptions about the normal distribution, ideas that may seem plausible but are mathematically untrue. For example, it is sometimes mistakenly thought that two linearly uncorrelated, normally distributed random variables must be statistically independent. However, this is ...
If X is a gamma(α, β) random variable and the shape parameter α is large relative to the scale parameter β, then X approximately has a normal random variable with the same mean and variance. If X is a Student's t random variable with a large number of degrees of freedom ν then X approximately has a standard normal distribution.
In the absolutely continuous case, probabilities are described by a probability density function, and the probability distribution is by definition the integral of the probability density function. [7] [4] [8] The normal distribution is a commonly encountered absolutely continuous
Uniform distribution may refer to: Continuous uniform distribution; Discrete uniform distribution; Uniform distribution (ecology) Equidistributed sequence; See also.
might hold, given some general sequence b k. One noteworthy result is that the sequence 2 k a mod 1 is uniformly distributed for almost all, but not all, irrational a. Similarly, for the sequence b k = 2 k a, for every irrational a, and almost all x, there exists a function ƒ for which the sum diverges.