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# Uniform Distribution

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Uniform Distribution

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### Uniform Distribution

1. 1. 1.8 Uniform Distribution<br />
2. 2. Rectangular or Uniform distribution<br />A random variable X is said to have a <br />continuous uniform distribution over an<br />interval (, ) if its probability density function <br />is constant k over entire range of x.<br />PROBABILITY DENSITY FUNCTION<br />f (x) = k,  &lt; X &lt; <br /> = 0 otherwise<br />
3. 3. Rectangular or Uniform distribution<br />The uniform distribution, with parameters  and , has probability density function <br />
4. 4. Figure:Graph of uniform probability density<br />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.<br />Uniform distribution<br />
5. 5. Distribution function for uniform density <br /> function<br />Uniform distribution<br />
6. 6. The Uniform Distribution<br />Mean of uniform distribution<br />Proof:<br />
7. 7. The Uniform Distribution<br />Variance of uniform distribution<br />Proof:<br />
8. 8. The Uniform Distribution<br />Moment generating function<br />
9. 9. Discrete Uniform distribution<br />If random variable assume finite no. of<br /> values with each value occuring with same<br /> probability <br />Probability density function is<br /> f(x) = 1/n, X=x1,x2,…… xn<br />