Question

Suppose that the expected number of accidents per week at an industrial plant is $5$. Suppose also that the numbers of workers injured in each accident are independent random variables with a common mean of $2.5$. If the number of workers injured in each accident is independent of the number of accidents that occur, compute the expected number of workers injured in a week .

Short answer

$E\left(NX\right)=12.5$

Step-by-step solution

Given information

Given in the question that, .Suppose that the expected number of accidents per week at an industrial plant is $5$. Suppose also that the numbers of workers injured in each accident are independent random variables with a common mean of $2.5$.

Explanation

Let $N$= number of accidents to happen in seven days. Allow $X=$to number of workers injured in every mishap. The quantity of workers injured in accidents each week should be $N\times X$. So we needs $E[NX]$

Since we know that $\mathrm{N}$and $\mathrm{X}$are independent, we know that

$Cov(N,X)=E\left(NX\right)-E\left(N\right)E\left(X\right)=0$

$\Rightarrow E\left(NX\right)=E\left(N\right)E\left(X\right)=5\times 2.5=12.5$

Final answer

The expected number of workers injured in a week is$E\left(NX\right)=12.5$