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## Homework Statement

4. Let X and Y have the joint probability distribution

(a) Find P(X +Y ≤ 4).

(b) Find the marginal probability distributions f1(x) and f2(y).

(c) Find P(X < 2|Y = 2).

(d) Are X and Y independent?

## The Attempt at a Solution

a) f(1,1) + f(1,2) + f(1,3) + f(2,1) + f(2,2) + f(3,1)

b) f1(1) = .1 + .05 + .15 = .3

f1(2) = .1 + .05 + .1 = .25

f1(3) = .15 + .2 + .1 = .45

f2(1) = .35

f2(2) = .3

f2(3) = .35

c) f(1,2) = .05

d) they are independent if f(x,y) = f1(x)f2(y) for all x and y

f(1,1) = .1 f1(1)f2(1) = .3(.35) = .105

they are not independent .

is this correct?