Uniform Distribution

1. 1.8 Uniform Distribution

2. Rectangular or Uniform distribution A random variable X is said to have a continuous uniform distribution over an interval (, ) if its probability density function is constant k over entire range of x. PROBABILITY DENSITY FUNCTION f (x) = k,  < X <  = 0 otherwise

3. Rectangular or Uniform distribution The uniform distribution, with parameters  and , has probability density function

4. Figure:Graph of uniform probability density All values of x from  to  are equally likely in the sense that the probability that x lies in an interval of width x entirely contained in the interval from  to  is equal to x/( - ), regardless of the exact location of the interval. Uniform distribution

5. Distribution function for uniform density function Uniform distribution

6. The Uniform Distribution Mean of uniform distribution Proof:

7. The Uniform Distribution Variance of uniform distribution Proof:

8. The Uniform Distribution Moment generating function

9. Discrete Uniform distribution If random variable assume finite no. of values with each value occuring with same probability Probability density function is f(x) = 1/n, X=x1,x2,…… xn