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Math Help - Join Probability & Random Variables

  1. #1
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    Join Probability & Random Variables

    Hello, I'm very confused how to solve this problem... since I'm very low at math maybe someone can help me.

    Assume a black bag containing 5 BLUE balls 3 RED balls and 2 GREEN balls. if we drew 2 balls arbitrarily from this black bag, using X to represent the number of BLUE balls drawn, and Y to represent the number of RED balls drawn, compute the following items :
    a. the joint probability function f(x,y);
    b. P[(X,Y) E A], where A is the region {(x,y)|x+y<=1}
    c.When Y=1, find f(x|y=1) (i.e the conditional distribution for X, when Y=1), then using it to determine P(X=0|Y=1);
    d.Prove this two random variables X and Y are not statistically independent

    I've try to answer the point a
    P(x,y) = P(x).P(x|x)+ P(x).P(y|x)+ P(y).P(y|y)+ P(y).P(x|y)

    but I'm not sure whether it's correct or not...

    Thanks in advance
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  2. #2
    MHF Contributor matheagle's Avatar
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    It all depends on what you do with the first ball.
    If you replace it, then this is a multinomial distribution.
    If you do not replace it, then it's a hypergeometric distribution.

    I don't know what
    P(x,y) = P(x).P(x|x)+ P(x).P(y|x)+ P(y).P(y|y)+ P(y).P(x|y)
    means.

    Look at
    http://www.mathhelpforum.com/math-he...-question.html
    because most likely, you are sampling without replacement and it just another hypergeometric.
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