# Zero inflated poisson

## Homework Statement

f(x) = (1-p)+pe^-lamdba ; x=0
= [p(e^-lambda)lambda^x]/x! ; x = 1, 2, ....
= 0 ; otherwise

## Homework Equations

show that f(x) is a valid probability function

## The Attempt at a Solution

I think I am supposed to integrate [p(e^-lambda)lambda^x]/x! from 0 to infinity...
or is it 1 - infinity? i'm very confused. Could someone help me solve this?

Thanks

Sorry if my notations are wrong, I'm new.