Suggested languages for you:

Americas

Europe

Q.15

Expert-verifiedFound in: Page 347

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

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

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

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

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

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

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,

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

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

$=0.83$

94% of StudySmarter users get better grades.

Sign up for free