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Uniform Distribution
 

Uniform Distribution

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Uniform Distribution

Uniform Distribution

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    Uniform Distribution Uniform Distribution Presentation Transcript

    • 1.8 Uniform Distribution
    • 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
    • Rectangular or Uniform distribution
      The uniform distribution, with parameters  and , has probability density function
    • 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
    • Distribution function for uniform density
      function
      Uniform distribution
    • The Uniform Distribution
      Mean of uniform distribution
      Proof:
    • The Uniform Distribution
      Variance of uniform distribution
      Proof:
    • The Uniform Distribution
      Moment generating function
    • 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