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Math Help - PmF

  1. #1
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    PmF

    A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Y is the number of heads in the last three tosses.

    Find the joint probability mass function and marginal probability mass function of X and Y.

    ON this problem, I did HHHH, HHHT, HHTH,....and so on. Is that how you start off and make a table from there. like there is a 1/13 chance of getting first three heads? I am not completely sure.
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  2. #2
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    Quote Originally Posted by durham2 View Post
    A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Y is the number of heads in the last three tosses.

    Find the joint probability mass function and marginal probability mass function of X and Y.

    ON this problem, I did HHHH, HHHT, HHTH,....and so on. Is that how you start off and make a table from there. like there is a 1/13 chance of getting first three heads? I am not completely sure.
    List all the outcomes and use these to set up a table with X along the top and Y along the side. By the way, probability that the first three are heads is Pr(HHHT) + Pr(HHHH) = 1/16 + 1/16 = 1/8 ....
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    Quote Originally Posted by mr fantastic View Post
    List all the outcomes and use these to set up a table with X along the top and Y along the side. By the way, probability that the first three are heads is Pr(HHHT) + Pr(HHHH) = 1/16 + 1/16 = 1/8 ....

    okk so you put all 16 outcomes in a table? or is it 0-4 for how many heads you can get?
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    Quote Originally Posted by durham2 View Post
    okk so you put all 16 outcomes in a table? or is it 0-4 for how many heads you can get?
    If
    X is the number of heads in the first three tosses
    then what is the minimum and maximum possible value of X?

    If
    the random variable Y is the number of heads in the last three tosses
    then what is the minimum and maximum possible value of Y?
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  5. #5
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    Quote Originally Posted by durham2 View Post
    okk so you put all 16 outcomes in a table? or is it 0-4 for how many heads you can get?
    For X,Y seperately 0-3 might be sufficient.
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