Uniform Distribution

8,710 views

Published on

Uniform Distribution

Published in: Technology
0 Comments
4 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
8,710
On SlideShare
0
From Embeds
0
Number of Embeds
21
Actions
Shares
0
Downloads
0
Comments
0
Likes
4
Embeds 0
No embeds

No notes for slide

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 />

×