Results 1 to 2 of 2

Math Help - Marginal distribution

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    132

    Marginal distribution

    For the following joint distribution

    ---Y
    X- 1-- 2
    0 .02 .08
    1 .11 .44
    2 .07 .28

    (i) Calculate the marginal distribution for each of X and Y
    (ii) Find
    a) P(X >= 1)
    b) P(X = 1 | Y = 2)
    (iii) Indicate if X and Y are independent, justifying your answer.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2008
    From
    Montreal
    Posts
    311
    Awards
    1
    for i)
    to find X you just have to sum across the rows, so you get:

     X_0 = 0.02+0.08 = 0.1
     X_1 = 0.11+0.44 = 0.55
     X_2 = 0.07+0.28 = 0.35

    and for Y you do the same thing across the columns, so you get:
     Y_1 = 0.02+0.11+0.07= 0.2
     Y_2 = 0.08 +0.44 +0.28 = 0.8

    for ii)
    a) so P(X\geq 1) = P(X=1) \ \cup \ P(X=2) = 0.55+0.35 = 0.9
    b) P(X=1|Y=2) = \frac{P(X=1 \ \cap \ Y=2)}{P(Y=2)} = \frac{0.44}{0.8} = \frac{11}{20}

    for iii)
    they're dependent, but I'm still trying to figure out why.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the marginal distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 22nd 2010, 06:39 AM
  2. marginal distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 4th 2010, 05:11 AM
  3. marginal distribution
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: October 19th 2010, 10:31 PM
  4. Marginal Distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 28th 2009, 11:43 PM
  5. Marginal and Conditional Distribution
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 30th 2007, 08:09 PM

Search Tags


/mathhelpforum @mathhelpforum