Question

$f\left(x\right)$a continuous probability function, is equal to $\frac{1}{3}$and the function is restricted to $1\le x\le 4$. Describe$P\left(x>\frac{3}{2}\right)$.

Short answer

The required probability is$P\left(x>\frac{3}{2}\right)$$=0.83$

Step-by-step solution

Given Information 

$f\left(x\right)$a continuous probability function is equal to $\frac{1}{3}$.

The function is restricted to $1\le x\le 4$.

We need to describe$P\left(x>\frac{3}{2}\right)$

Calculation

Here $X$follows a uniform distribution.

The area between $1\le x\le 4$forms a rectangle with $X$axis

Here,

$\text{Height}=\frac{1}{3}$

$\text{Base}=4-\frac{3}{2}$

$=\frac{8-3}{2}$

$=2.5$

Therefore, the required probability is,

$P\left(x>\frac{3}{2}\right)=\text{Base}\times \text{Height}$

$=\left(2.5\right)\times \left(\frac{1}{3}\right)$

$=0.83$