Question

$f\left(x\right)$for a continuous probability function is$15$ , and the function is restricted to $0\le x\le 5$. What is $P(x<0)$?

Short answer

The value of the$P(x<0)$iszero.

Step-by-step solution

Given information

$f\left(x\right)$for a continuous probability function is $15$

The function is restricted to$0\le x\le 5$

Solution

Here, the probability density function of the continuous random variable $X$is defined as:

$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{5},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\le x\le 5\\ 0,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{otherwise}\end{array}\right.$

So, the probability value of $P(x<0)$will be calculated as:

$P(x<0)=1-P(x\ge 0)$

$=1-{\int }_0^5 \frac{1}{5}dx$

$=1-\frac{1}{5}[x{]}_0^5$

$=1-\frac{1}{5}[5-0]$

$=0$