Project ForgeEngineering Mathematics
Calculus
GATE 2022
Medium
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).
0.18(± 0.01 accepted)
Explanation
P(X=k)=e^(−λ)λᵏ/k!. Setting P(1)=P(2): λe^(−λ) = (λ²/2)e^(−λ) → λ=2. Then P(3) = λ³e^(−λ)/3! = 8e^(−2)/6 ≈ 1.3333×0.135335 ≈ 0.18.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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