Joint probability distribution

  • #1
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Homework Statement


4. Let X and Y have the joint probability distribution

Screen Shot 2015-10-19 at 5.45.15 PM.png




(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?
 

Answers and Replies

  • #2
andrewkirk
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It looks right to me.
 
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  • #3
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thanks!
 

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