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## Homework Statement

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.