Results 1 to 2 of 2

Math Help - probability-discrete randon variables, pmfs

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    68

    Thumbs down probability-discrete randon variables, pmfs

    I've never even covered this stuff before guys :S The below numbers where in a table but I couldnt recreate it on here , hope you clever people can figure it out

    Discrete random variables X and Y have joint probability mass function:

    Y=0 & X=0 =>0.2
    Y=1 & X=0 =>0.2
    Y=2 & X=0 =>0.1
    Y=0 & X=1 =>0.2
    Y=1 & X=1 =>0.3
    Y=2 & X=1 =>0.0

    (a) Find the marginal means and variances of both X and Y .
    (b) Find the conditional mean of Y given X = 1.
    (c) Find the correlation between X and Y
    Last edited by mitch_nufc; February 22nd 2009 at 03:24 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    To get the marginal distribution of just one rv, you need to sum over the other one.
    For example P(Y=0)=P(Y=0 and X=0) + P(Y=0 and X=1)=.4
    You are summing over all values of x
    P(Y=1)=P(Y=1 and X=0) + P(Y=1 and X=1)=.5
    Since these probabilities sum to one
    we have .1 left over for P(Y=2)
    The last probability, Y=3 & X=1 =>0 should be erased.
    Anything that has probably zero shouldn't be listed.
    From here you should be able to get Y's mean and variance.
    As for the conditional mean of Y when X=1,
    you need the distribution of Y when X=1.
    You only need these two
    Y=0 & X=1 =>0.2
    Y=1 & X=1 =>0.3
    P(Y=0|X=1)=P(Y=0and X=1)/P(X=1)=.2/.5=.4
    Thus P(Y=1|X=1)=1-P(Y=0|X=1)=.6
    So, E(Y|X=1)=(0)(.4)+(1)(.6)=.6
    The correlation between two rvs is the covariance divided by the st deviations
    AND by the Cauchy-Schwarz inequality it has to be between -1 and 1.
    Last edited by matheagle; February 22nd 2009 at 06:17 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: November 4th 2010, 06:22 PM
  2. Replies: 1
    Last Post: April 6th 2010, 11:30 AM
  3. Normal randon varible
    Posted in the Statistics Forum
    Replies: 1
    Last Post: February 7th 2010, 04:24 PM
  4. Joint PMFs of Multiple Random Variables - Urgent Help
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 21st 2009, 09:28 AM
  5. Discrete Variables
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 12th 2008, 12:34 AM

Search Tags


/mathhelpforum @mathhelpforum