Answer to Question #248363 in Statistics and Probability for Vishnu kishore

Question

A posion distribution has double mode at x=2 and x=3 .what is the probability that x will have one or other of the two values

Answer 1

If the Poisson distribution is bimodal, the two modes are at the points x=λ-1 and x=λ, where λ is the parameter of the Poisson distribution.

$x=1 \\ x=2 \\ λ=2 \\ P(X=x) = \frac{e^{-λ}λ^x}{x!} \\ P(X=1) = 2e^{-2} \\ P(X=2) = \frac{e^{-2}2^2}{2!} = 2e^{-2}$

Required probability $= P(X=1) + P(X=2) = 2e^{-2} +2e^{-2} = 0.542$