IFT Notes for Level I CFA^{®} Program

## R09 Common Probability Distributions

# 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 x_{1} and x_{2}, where x_{1} and x_{2} both lie within the range is given by:

P(x

_{1} ≤ X ≤ x

_{2}) =

**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%.

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