Validating the Probability Function f(x) for Zero-Inflated Poisson Distribution

[mekhi]

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.

 

[mekhi]

sorry, I've now worked it out. I used the summation instead of the integral. i hope this is correct.

thanks