GATE Mechanical 2023 | Question: 1

Question

A machine produces a defective component with a probability of $0.015$. The number of defective components in a packed box containing $200$ components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are

• A. $3$ and $3$, respectively
• B. $\sqrt{3}$ and $\sqrt{3}$, respectively
• C. $0.015$ and $0.015$, respectively
• D. $3$ and $9$, respectively

Answer 1

To find the mean and variance of the Poisson distribution for the number of defective components in a packed box containing 200 components produced by the machine, we can use the following formulas:

1. Mean (μ) = λ
2. Variance (σ^2) = λ

Where λ is the average rate of occurrence, which in this case is the product of the probability of a defective component (0.015) and the total number of components in the box (200):

λ = 0.015 * 200 = 3

So, the mean (μ) is 3, and the variance (σ^2) is also 3.

Therefore, the correct answer is (A) 3 and 3, respectively.