Uniform Distribution definition, formula and applications

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Uniform Distribution

There are various continuous probability distributions such as uniform distribution, normal distribution, exponential distribution, gamma distribution, beta distribution, weibul distribution, cauchy distribution ect. Uniform distribution is a univariate continuous probability distribution with two parameter a and b.
A continuous random variable x is said to have a uniform distribution if the probability function is defined by-

where, a and b are the two parameters of the distribution such that -∞<=a<=b<=∞.

Properties

There are some impotant properties of uniform distribution-
• The mean of uniform distribution is
• The median of uniform distribution is .
• The variance of uniform distribution is  (b-a)∧2/12.
• The mode of uniform distribution is  any value of.
• The skewness of uniform distribution is 0.
• The kurtosis of uniform distribution is .

Special characteristics of Uniform distribution

Some special characteristics of uniform distribution are given below-
• The probability of this distribution is same for equal intervals in any part of the distribution.
• The probability of uniform distribution depends on the length of the intervals, not on its position.
• The pdf of the uniform distribution over the interval [0,1] is defined by f(x)=1.
• Moreover, uniform distribution can be defined in a infinite number of ways.