Question

Use the following information to answer the next seven exercises. A distribution is given as $X~Exp(0.75)$. Which is larger, the mean or the median?

Short answer

Mean is greater than median in this summation.

Step-by-step solution

Function of cumulative distribution 

As the rule of commutative distribution

$P(X<x)=1-e^{-mx}$

It has been mentioned that

$X~Exp(0.75)$

So,$m=0.75$

Formula of cumulative distribution 

As media has been considered as the percentile

Formula of cumulative distribution is

$P(x<k)=1-e^{-0.75k}$

Applying all data

$0.50=1-e^{0.75k}$

$e^{0.75k}=0.50$

Equation of cumulative distribution 

Applying logarithm in both sides

$$\begin{gathered} \ln \left(e^{-0.75k}\right)=\ln (0.50) \\ k=0.9241 \end{gathered}$$

The expression of mean is

$\mu =\frac{1}{m}$

Applying all data

$\mu =\frac{1}{0.75}=1.33$