The continuous uniform distribution is defined over a range from a lower limit ‘a’ to an upper limit ‘b’. These limits serve as the parameters of the distribution.
The probability that the random variable will take a value between x1 and x2, where x1 and x2 both lie within the range is given by:
Example
X is a uniformly distributed continuous random variable between 10 and 20. Calculate the probability that X will fall between 12 and 18.
Solution:
The cumulative distribution function for a continuous random variable is shown below:
Example
A commodity analyst predicts that the price per ounce of gold three years from now will be between $1,500 and $1,700. Assume gold prices follow a continuous uniform distribution. What is the probability that the price will be less than $1,600 three years from now?
Solution:
F(1,600) = 
. The probability that gold price will be less than $1,600 per ounce three years from now is 50%.
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