# Statistics - Continuous Uniform Distribution

The continuous uniform distribution is the probability distribution of random number selection from the continuous interval between a and b. Its density function is defined by the following. Here is a graph of the continuous uniform distribution with a = 1, b = 3.

## Formula

f(x) = \begin{cases} 1/(b-a), & \text{when $a \le x \le b$} \\ 0, & \text{when $x \lt a$ or $x \gt b$} \end{cases}

### Example

Problem Statement:

Suppose you are leading a test and present an inquiry on the crowd of 20 contenders. The time permitted to answer the inquiry is 30 seconds. What number of persons is prone to react inside of 5 seconds? (Regularly, the contenders are required to click a catch of the right decision and the champ is picked on the premise of first snap).

Solution:

Step 1: The interval of the probability distribution in seconds is [0, 30].

⇒ The probability density is = 1/30-0=1/30.


Step 2: The requirement is how many will respond in 5 seconds. That is, the sub interval of the successful event is [0, 5]. Now the probability P (x < 5) is the proportion of the widths of these two interval.

⇒ 5/30=1/6.


Subsequent to there are 20 contenders, the quantity of contenders prone to react in 5 seconds is (1/6) (20) =3.