GATE 2022 ME (ME1) – Question 47
Let a random variable X follow Poisson distribution such that Prob($X = 1$) = Prob($X = 2$). The value of Prob($X = 3$) is __________ (round off to 2 decimal places).
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Correct answer: 0.17 to 0.19
Explanation
For a Poisson distribution $P(X = k) = \frac{e^{-\lambda}\lambda^k}{k!}$. $P(1) = P(2)$ gives $\lambda = \frac{\lambda^2}{2}$, so $\lambda = 2$. Then $P(3) = \frac{e^{-2} \times 8}{6} = 0.1804$.