IFT Notes for Level I CFA® Program
IFT Notes for Level I CFA® Program

# Part 2

## 3. Continuous Random Variables

### 3.1.     Continuous Uniform Distribution

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:

P(x1 ≤ X ≤ x2) =

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:

P(12 ≤ X ≤ 18) =

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%.