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Uniform distribution

  • The simplest continuous distribution function is the uniform distribution. This is defined over a range of values for x, a ≤ x ≤ b
  • The density function is:
    • f (x) =1 / (b− a), a ≤ x ≤ b
  • Its mean and variance are given by:
    • E(X) =(a + b) / 2
    • V(X) = (b− a)2 / 12



  • Assume we use continuous uniform distribution U(0,10) to generate a series of random numbers. Which of the following statements is Correct?
  • The number 5 is likely to be observed much more often than any other number
  • Numbers between 4 and 6 are more likely to occur than the number between 6 and 10, because the first interval is closer to the center of the distribution
  • Numbers between 1 and 3 are as likely as the number between 4 and 6
  • Numbers between 1 and 3 are less likely than the number between 4 and 6, due to skewness of
  • the distribution



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