A Poisson distribution is such that the probability is the s

A Poisson distribution is such that the probability is the same for X = 1 and X = 2. What is this probability?

Solution

Note that for a Poisson distribution,

P(x) = u^x e^(-u)/x!

Thus,

P(0) = e(-u)
P(1) = u (e^-u)

Thus,

u(e^-u) = e^(-u)

e^(-u) (1-u) = 0

Thus,

u = 1

Thus,

P(0) = P(1) = e^(-1) = 0.367879441 [ANSWER]