Question

Use the following information to answer the next ten exercises.A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: $\begin{array}{rcl}& & X~Exp(0.2)\end{array}$

State the probability density function.

Short answer

The probability density function of the given expression is$f\left(x\right)=0.2e^{-0.2x}$

Step-by-step solution

Definition

A probability distribution (the likelihood of a result) for a discrete random variable is defined by the Probability Density Function, which is a statistical expression.

Concept and Formula of Probability Density Function 

General form of Probability Density Function of Exponential Distribution is:

$f\left(x\right)=m{e}^{-mx}$

Finding the Probability Density Function 

The given Exponential Distribution is, $X~Exp(0.2)$

Here $m=0.2$

Probability Density Function of Exponential Distribution is $f\left(x\right)=m{e}^{-mx}$

Putting the value of $m=0.2$we get,

role="math" localid="1648192596517" $f\left(x\right)=0.2e^{-0.2x}$

The above expression represents the Probability Density Function of the given expression.