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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<=∞.
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.