## Quick Reference

The uniform distribution on the interval [*a*, *b*] is the continuous probability distribution whose probability density function *f* is given by *f*(*x*)=1/(*b*−*a*), where *a*≤*x*≤*b*. It has mean (*a*+*b*)/2 and variance (*b*−*a*)^{2}/12. There is also a discrete form: on the set 1, 2,…, *n*, it is the probability distribution whose probability mass function is given by Pr(X=*r*)=1/2, for *r*=1, 2,…, *n*. For example, the random variable for the winning number in a lottery has a uniform distribution on the set of all the numbers entered in the lottery.

*Subjects:*
Probability and Statistics.

## Related content in Oxford Index

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.