Question

X ~ _____(_____,_____)

Short answer

The required value is$X~P\left(8\right)$.

Step-by-step solution

:Given

Eighteen teens on average dies due to motor vehicle accident every day.

:Interpretation

$X$is a random variable who represents the no. of teens who die because of motor vehicle injuries. $X$can take any value $0,1,2,3,4\dots$

According to the given situation, we can clearly say that $X$follows the Poisson Distribution with parameter mean $\left(\lambda \right)$is 8 per day and variance $\left(\lambda \right)$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 occurrence of no. of events in a fixed time interval is fixed.

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