Results 1 to 2 of 2

Math Help - Combining two dependant discrete random variables

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    1

    Combining two dependant discrete random variables

    Hi,
    Im looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables.
    This would be easy if they were independent, but theyre not. There is a known correlation between the variables.

    Question: how to combine two discrete random variables with correlation?
    Given: The marginal probabilities of the two variables & a correlation function
    Result: either the individual probabilities in a probability table or the complete probability distribution of the combination.

    Simple example:
    Variables A and B are the distributions:
    PA(a=1, 4) = [0.75, 0.25]
    PB(b=4, 8, 10) = [0.25, 0.25, 0.5]

    Their joint probability function is shown in their joint probability table and joint value table:
    P B=4 8 10
    A=1 ? ? ? 0.75
    4 ? ? ? 0.25
    0.25 0.25 0.5 1

    value B=4 8 10
    A=1 4 8 10
    4 16 32 40

    (tables are clearer in attached file)

    The correlation between the two variables is: b = 10 2/3*a

    P(A*B)(4, 8, 10, 16, 32, 40) = ?
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Combining two dependant discrete random variables

    Quote Originally Posted by simcc View Post
    Hi,
    Im looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables.
    This would be easy if they were independent, but theyre not. There is a known correlation between the variables.

    Question: how to combine two discrete random variables with correlation?
    Given: The marginal probabilities of the two variables & a correlation function
    Result: either the individual probabilities in a probability table or the complete probability distribution of the combination.

    Simple example:
    Variables A and B are the distributions:
    PA(a=1, 4) = [0.75, 0.25]
    PB(b=4, 8, 10) = [0.25, 0.25, 0.5]

    Their joint probability function is shown in their joint probability table and joint value table:
    P B=4 8 10
    A=1 ? ? ? 0.75
    4 ? ? ? 0.25
    0.25 0.25 0.5 1

    value B=4 8 10
    A=1 4 8 10
    4 16 32 40

    (tables are clearer in attached file)

    The correlation between the two variables is: b = 10 2/3*a

    P(A*B)(4, 8, 10, 16, 32, 40) = ?
    What you have called a correlation is a functional relation between the values of the random variables, the correlation is a number E((a-\overline{a})(b-\overline{b})). The relation is impossible in the form you present it.

    Now assuming that you have the actual correlation:

    Since two of the cells can be assigned arbitrarily within the constraints of the marginals the joint distribution has two degrees of freedom.

    The correlation gives you one equation in the two variables that represent the degrees of freedom.

    Usually a single equation in two real variables does not have a unique solution, and that is very likely the case here (it is possible that there is a unique solution but you won't know untill you so the calculations).

    You almost certainly will need an additional constraint to get a unique solution.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Discrete random variables
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: October 11th 2010, 11:15 AM
  2. Discrete random variables (2)
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: October 11th 2010, 10:31 AM
  3. help with discrete random variables
    Posted in the Statistics Forum
    Replies: 7
    Last Post: October 2nd 2010, 10:55 PM
  4. Discrete Random Variables
    Posted in the Statistics Forum
    Replies: 4
    Last Post: April 13th 2010, 03:39 AM
  5. Replies: 3
    Last Post: January 13th 2010, 11:44 AM

Search Tags


/mathhelpforum @mathhelpforum