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Math Help - joint density function

  1. #1
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    joint density function

    An unbiased coin is tossed three times. Let X be the number of heads on the first toss and Y the number of heads on the second and third tosses combined. Find the joint density function of X and Y.

    Hmm i reckon I'm wrong but is the correct answer 1/2?

    SOrry i don't know how to draw a table here but all i did for this question was add up the row total??
    so 1/8 + 1/4 + 1/8

    _____Y______
    _____0____1_____2
    0 |....1/8...1/4....1/8
    1 |....1/8...1/4...1/8 | X


    P(X = 0, Y=0) = 1/8
    P(X=0, Y=1) = 1/4
    P(X=0,Y=2) = 1/8

    which equals to 1/2... is this what I'm supposed to do or am i way off(highly likely)?

    Yeahhh and here are the possibilities i drew up:
    ____X Y
    HHH 1 2
    HHT 1 1
    HTH 1 1
    THH 0 2
    HTT 1 0
    THT 0 1
    TTH 0 1
    TTT 0 0
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  2. #2
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    Quote Originally Posted by gconfused View Post
    An unbiased coin is tossed three times. Let X be the number of heads on the first toss and Y the number of heads on the second and third tosses combined. Find the joint density function of X and Y.

    Hmm i reckon I'm wrong but is the correct answer 1/2? Mr F says: Answer to what?? The joint density function is the table you drew below (which is correct, by the way). I don't see any other question in your post ....?

    SOrry i don't know how to draw a table here but all i did for this question was add up the row total??
    so 1/8 + 1/4 + 1/8

    _____Y______
    _____0____1_____2
    0 |....1/8...1/4....1/8
    1 |....1/8...1/4...1/8 | X


    P(X = 0, Y=0) = 1/8
    P(X=0, Y=1) = 1/4
    P(X=0,Y=2) = 1/8

    which equals to 1/2... is this what I'm supposed to do or am i way off(highly likely)?

    Yeahhh and here are the possibilities i drew up:
    ____X Y
    HHH 1 2
    HHT 1 1
    HTH 1 1
    THH 0 2
    HTT 1 0
    THT 0 1
    TTH 0 1
    TTT 0 0
    ..
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  3. #3
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    oh im so dumb i thought i was supposed to get a value haha
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