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Math Help - Basic Joint Distribution Question

  1. #1
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    Basic Joint Distribution Question

    G'day! I have the answer to this question but I do NOT understand it. Any help much appreciated...
    Three Players play 10 independent rounds of a game. Each player has probability \frac{1}{3} of winning each round.
    Find the joint distribution of the numbers of games won by each of the players.

    I am having immense difficulty with this joint probability stuff. if f_{XYZ} (x,y,z) = P_{XYZ} (x,y,z) I assume then that, for example P_{XYZ} (x,y,z) = P_{XYZ} (1,0,0) means the probability of player x winning 1 game and players y,z winning no games? This then could only account for one round? I am totally lost!!!
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  2. #2
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    Re: Basic Joint Distribution Question

    The question is asking you to find p(x,y,z), where x+y+z = 10 and x is the number of games won by the first player, y the number won by the second player, and z the number own by the third player. For any other values of x,y,z (not summing to 10), the probability is zero.
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