Please help out

Question

A random variable X has poisson distribution with mean equal to 0.4.what is the probability that the random variable is greater than Zero?

Answer 1

The first important thing to realize, is that a Poisson distribution is discrete. X can take the values 0, 1, 2, 3, ..., ∞

Next, it's important to realize that "greater than zero" is the complement of "exactly 0." P(X > 0) and P(X = 0) must sum to 1, because it is the sum of every probability in the distribution.

P(X > 0) = 1 - P(X = 0) = 1 - 0.4⁰ * e^-0.4/0! = 1 - e^-0.4 ≈ 0.3297.

If you don't know where I got that formula from, look up the pmf of the Poisson distribution. I just substituted in lambda = 0.4 and x = 0.