Suppose that the expected number of accidents per week at an industrial plant is 4. The number of workers injured in each accident is independent random variable with a common mean of 2. Assume also that the number of workers injured in each accident is independent of the number of accidents that occur. The expected number of injuries during a week isa)2b)4c)6d)8Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Given information:
- The expected number of accidents per week at an industrial plant is 4.
- The number of workers injured in each accident is independent random variable with a common mean of 2.
- The number of workers injured in each accident is independent of the number of accidents that occur.

To find:
The expected number of injuries during a week.

Explanation:
The expected number of injuries during a week can be found by multiplying the expected number of accidents per week by the expected number of injuries in each accident.

Step 1: Find the expected number of accidents per week:
The given information states that the expected number of accidents per week is 4. Therefore, the expected number of accidents per week is 4.

Step 2: Find the expected number of injuries in each accident:
The given information states that the number of workers injured in each accident is an independent random variable with a common mean of 2. Therefore, the expected number of injuries in each accident is 2.

Step 3: Calculate the expected number of injuries during a week:
To calculate the expected number of injuries during a week, we multiply the expected number of accidents per week by the expected number of injuries in each accident.

Expected number of injuries during a week = (Expected number of accidents per week) * (Expected number of injuries in each accident)
= 4 * 2
= 8

Therefore, the expected number of injuries during a week is 8.

Answer:
The correct answer is option D) 8.

Similar Mathematics Doubts

We make n independent trials in each of which an event A may occur with probability p. A random variable X is defined as the number of occurrences of the event A in all the n trials. The variance of X is

If X1and X2 are independent normal random variables with parameters respectively then X1 - X2is normal with meanμand varianceσ2such that

Let X be a randon variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean –1 and variance unknown. If P(X ≤ –1) = P(Y ≥ 2) the standard deviation of Y is

Let X and Y be independent Poisson random variables with parameters 5 and μ, respectively. IfP(XY= 1) = P(X+ Y= 1),then Var(Y) is

Analysis of variance is concerned with

Top Courses for Mathematics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams