Understanding the cdf of a Sum of Independent Random Variables

[suuperhiroo]

I am have trouble with a question, and how exactly each given part of this question relates to getting the answer.



1. The problemb]

Assume that N,X₁, X₂...are independent.

Let P(N = k) = q^k-1p , k$$\geq1$$, p+q = 1
and let X₁,X₂,X₃,...be iid with a common pdf


f(x) = { $$\lambda$$e^{-$$\lambda$$x}, x$$\geq0$$

​

{ 0, x$$\leq0$$

*e is raised to the power of 'negative lambda times x'

What theories and concepts should i be familiar with to answer this question? I have studied the chapters up to the ones dealing with Random Variables, as well as Continuous Random variables, yet this question is still not within my reach of solving, or even understanding for that matter. How do i use the given information to create a cdf?

 

[Roni1985]

what's the question ?

looks like the first one is a geometric r.v. (discrete) and the second one is an exponential r.v. (continuous).

 

[suuperhiroo]

im sorry. I didnt put the question.

I am asked to : Find the the cdf of X₁+ X₂...X_N