Question

If \(X\) is a random Poisson variate with \(P(X=1) = P(X=2)\). Then \(P(X=4)\) is:

• A. \(\frac{2e^{-2}}{3}\)
• B. \(\frac{e^{-2}}{3}\)
• C. \(\frac{4e^{-2}}{3}\)
• D. \(\frac{2e^{-3}}{6}\)

Hint:

For any Poisson distribution, if \(P(X = k) = P(X = k+1)\), then the parameter \(\lambda\) is simply equal to \(k+1\).
Here, \(P(X = 1) = P(X = 2) \implies \lambda = 1 + 1 = 2\). This saves time on algebra.

Answer 1

The Correct Option is A