Find p (x = 4) if x has a poisson distribution such that 3p (x = 1) = p (x = 2).

The formula for Poisson distribution is:

P (x) = e^-k * k^x / x!

We know that:

3P (x = 1) = P (x = 2)

Therefore:

3 [e^-k * k^1 / 1!] = e^-k * k^2 / 2!

Simplifying by cancelling similar terms:

3 / 1! = k / 2!

k = 3 * 2! / 1!

k = 6

So at x = 4:

P (x = 4) = e^-6 * 6^4 / 4!

P (x = 4) = 0.1339 or 13.39%