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Chapter 7: Q.57 (page 356)

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

Expert verified

E(NX)=12.5

Step by step solution

01

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.

02

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×X. So we needs E[NX]

Since we know that Nand Xare independent, we know that

Cov(N,X)=E(NX)-E(N)E(X)=0

⇒E(NX)=E(N)E(X)=5×2.5=12.5

03

Final answer

The expected number of workers injured in a week isE(NX)=12.5

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