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GATE 2023 ME – Question 11

Engineering Mathematics · Probability and Statistics: Mean, median, mode, standard deviation, random variables and distributions · 1 mark · Multiple choice

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

  1. 3 and 3, respectively
  2. $\sqrt{3}$ and $\sqrt{3}$, respectively
  3. 0.015 and 0.015, respectively
  4. 3 and 9, respectively

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Correct answer: (A) 3 and 3, respectively

Explanation

The Poisson parameter is $\lambda = np = 200 \times 0.015 = 3$. For a Poisson distribution the mean and the variance are both equal to $\lambda$, so both are 3.