Question

Use the following information to answer the next seven exercises. A distribution is given as $X~Exp(0.75)$. Find$P(x<4)$

Short answer

The value of $P(x<4)$is$0.9502$

Step-by-step solution

Definition of cumulative distribution function

Cumulative Distribution Function of Exponential Distribution is represented as;

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

As per given information, $X~Exp(0.75)$

Therefore,$m=0.75$

Finding P(x < 4)

Calculation of required probability

$\begin{array}{rcl}P(x& <& 4)=1-e^{-0.75\times 4}\\ & =& 1-e^{-3}\\ & =& 1-0.0498\\ & =& 0.9502\end{array}$

Thus it can be said that$P(x<4)$is$0.9502$