Probability function

[aurao2003]

1. The problem statement, all variables and given/known data
Hi
I am trying to solve the d, e and f parts of this problem

The discrete random variable X has probability function
where k is a positive constant.

P(X = x) ={k(2 – x), x = 0, 1, 2,
k(x – 2), x = 3,
0, otherwise,

(a) Show that k = 0.25.
(b) Find E(X) and show that E(X 2) = 2.5.
(c) Find Var(3X – 2).
Two independent observations X1 and X2 are made of X.
(d) Show that P(X1 + X2 = 5) = 0.
(e) Find the complete probability function for X1 + X2.
(f) Find P(1.3 < X1 + X2 < 3.2).

Not sure how to begin. Please help. The exam is tomorrow.



2. Relevant equations



3. The attempt at a solution

[jbunniii]

For (a), what must be the answer if you sum P(X = x) over x = 0, 1, 2, 3?