$X_1,X_2,...\sim Pois(7), $ and independent random variables. $Y \sim Geom(1/4)$ independent from the $X_i$.
My question is the characteristic function of: $X_1+X_2+...+X_Y$
Can someone tell me how to do this.
I could do it if the sum went to some $n$, but I have no idea how to this.