Question

Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

Write the probability density function

Short answer

The Probability distribution function is$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{9},0.5<x<9.5\\ 0,Otherwise\end{array}\right.$

Step-by-step solution

Given Scenario

As per the given scenario;

the age of cars in staff parking lot considered to be uniformly distributed.

Suppose the age of the acrs in suburban college is denoted with X, hence x can be considered as intervals.

$=0.5<x<9.5$

Calculation of Probability Distribution function

As per the above consideration probability distribution function will be;

$\begin{array}{rcl}f\left(x\right)& =& \frac{1}{b-a}\\ & =& \frac{1}{9.5-0.5}\\ & =& \frac{1}{9}\end{array}$

Therefore the probability distribution function can be represented as;

$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{9},0.5<x<9.5\\ 0,Otherwise\end{array}\right.$