Let \( X \) follow Poisson distribution with mean \( \lambda \). If
\[P(X = 2) = \frac{1}{2} P(X = 3),\] then the value of \( \lambda \) is:
6
Using the Poisson distribution probability formula:
\( P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} \)
Substitute the given conditions \( P(X = 2) = \frac{1}{2} P(X = 3) \) and solve for \( \lambda \). The result gives \( \lambda = 6 \).
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