# Uniform distribution

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

Example
• 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
Solution

C.