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Joint probability distribution

  1. Oct 19, 2015 #1
    1. The problem statement, all variables and given/known data
    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?

    3. 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?
     
  2. jcsd
  3. Oct 19, 2015 #2

    andrewkirk

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    It looks right to me.
     
  4. Oct 19, 2015 #3
    thanks!
     
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