$P(X=1) = \lambda e^{-\lambda}$, $P(X=2) = \frac{\lambda^2 e^{-\lambda}}{2}$
Setting equal: $\lambda = \frac{\lambda^2}{2} \Rightarrow \lambda = 2$
Back to JEE Main 2026 Probability & Statistics
JEE Main 2026 — Mathematics Probability & Statistics
hard
mcq
2026
Official previous-year question
Verified 30 May 2026.
Question
If $X$ follows a Poisson distribution and $P(X=1) = P(X=2)$, then the mean of the distribution is:
Options
- A
$2$
- B
$1$
- C
$3$
- D
$\frac{1}{2}$
Solution
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