Question

What values does X take on?

Short answer

$X$can take any positive integer value from zero to positive perpetuity.
$X=0,1,2,3,4,\dots \dots$

Step-by-step solution

:Given

Eighteen teens on mean dies due to engine instrument casualty every day.

Explanation

$X$is a arbitrary variable who represents the no. of teens who die because of motor vehicle injuries. $\mathbf{X}$can take any value $0,1,2,3,4\dots ..$
According to the given situation, we can easily say that $X$
follows the Poisson Distribution with parameter mean $\left(\lambda \right)$is 8 per day and friction$\left(\lambda \right)$ is also 8 per day. In Poisson distribution Variance is equals to mean.
Poisson distribution occurs when there is not definite no. of trials or $n\to \infty$and circumstance of no. of events in a fixed time interval is fixed.

Probability mass function of Poisson distribution is: $P(X=x)=\frac{e^{\lambda }{x}^x}{x!}x=0,1,2,3,4,....$