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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-

$f\left&space;(&space;x;a,b&space;\right&space;)=\frac{1}{b-a};&space;a\leq&space;x\leq&space;b$

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.

### Releated

#### Probability Distributions in Statistics

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Spread the love          In statistics, probability distributions are very important measure which related to the random variable and statistical data. Every data patern follows a probability distribution. Continuous data follow the continuous distribution and discrete data follow the discrete distributions. According to wikipedia, “In probability theory and statistics, a probability distribution is the mathematical function that […]

#### Gamma Distribution definition, formula and applications

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Spread the love          In probabilistic statistics, the gamma distribution is a two-parameter family of continuous probability distributions which is widely used in different sectors. The exponential distribution, Erlang distribution, and chi-square distribution are special cases of it. Gamma Distribution A continuous random variable X is said to have a generalised gamma distribution with parameter α and […]