Question

Use the following information to answer the next seven exercises. A distribution is given as$X~Exp(0.75).$ Find the median.

Short answer

The value of median is 0.9241

Step-by-step solution

Function of  commutative distribution 

The rule of commutative distribution

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

As it has been given

$X~Exp(0.75)$

so$m=0.75$

Formula of  median commutative distribution 

The median commutative distribution has been considered as 50 percentile

Formula of median commutative distribution

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

Applying all data

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

$e^{-0.75k}=0.50$

Equation of  median commutative distribution 

Applying logarithm in both sides

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