GATE ME 2023 Set 1 — Question 11
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Engineering Mathematics → Statistics & Distributions → Poisson Distribution
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Question
A machine produces a defective component with a probability of . The number of defective components in a packed box containing components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are
Correct answer
(A) 3 and 3, respectively
Solution
For a binomial distribution with large and small , it can be approximated by a Poisson distribution where the parameter .
Given:
Mean () of Poisson distribution = .A key property of the Poisson distribution is that its mean is equal to its variance.
Variance () = .Therefore, the mean and variance are and , respectively.
Given:
Mean () of Poisson distribution = .A key property of the Poisson distribution is that its mean is equal to its variance.
Variance () = .Therefore, the mean and variance are and , respectively.
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