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Math Help - Joint PMFs of Multiple Random Variables - Urgent Help

  1. #1
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    Question Joint PMFs of Multiple Random Variables - Urgent Help

    It says my answers are incorrect. Can anyone help me please? What did I do wrong..?

    On a given day, your golf score takes values from range 100 to 109, with probability 0.1, independently from other days. Determined to improve your score, you decide to play on three different days and declare as your score the minimum X of the scores X1, X2, X3 on the different days.

    1. Calculate the PMF of X.
      pX(107)=

      pX(107)=comb(3,1)*0.1*0.3*0.3=0.027

      Px(k)=P(X>k-1)- P(X>k)
      Where P(X>k) = P(X1>k, X2>k, X3>k)=(109-k)^3*/(10^3)
    2. pX(101)=

      pX(101)= comb(3,1)*0.1*0.9*0.9=0.243;
    3. By how much has your expected score changed as a result of playing on three days?

      If PX(100+i)=0.3*(1-i)^2 then E(X)=102.475
      If P(X.1 then E(X)=104.5 Difference=102.475-104.5=-2.025
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  2. #2
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    Counting

    To get a score of 107 in the new 'minimum' fashion, he can only get scores of 107, 108 or 109 on the 3 days. The probability of getting a 107 is 0.1, the probability of getting a 108 or 109 is 0.2. His scores could have been:

    aaa - 3 scores of 107
    aab - 2 scores of 107, and 1 of 108 or 109
    abb - 1 scores of 107, and 2 of 108 or 109.

    aaa - happens in 1 way
    aab - happens in 3 ways.
    abb - happens in 3 ways.

    aaa - probability = 0.1*0.1*0.1=0.001
    aab - probability = 0.1*0.1*0.2=0.002
    abb - probability = 0.1*0.2*0.2=0.004

    So the total probability for 107 is:
    1*0.001 + 3*0.002 + 3*0.004 = 0.019
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  3. #3
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    Quote Originally Posted by qmech View Post
    To get a score of 107 in the new 'minimum' fashion, he can only get scores of 107, 108 or 109 on the 3 days. The probability of getting a 107 is 0.1, the probability of getting a 108 or 109 is 0.2. His scores could have been:

    aaa - 3 scores of 107
    aab - 2 scores of 107, and 1 of 108 or 109
    abb - 1 scores of 107, and 2 of 108 or 109.

    aaa - happens in 1 way
    aab - happens in 3 ways.
    abb - happens in 3 ways.

    aaa - probability = 0.1*0.1*0.1=0.001
    aab - probability = 0.1*0.1*0.2=0.002
    abb - probability = 0.1*0.2*0.2=0.004

    So the total probability for 107 is:
    1*0.001 + 3*0.002 + 3*0.004 = 0.019
    Thank you...And, how can I compute the probability of 101?
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  4. #4
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    Method's the same, just different numbers

    The probability of the score 101 is still 0.1, but the probability of getting a larger score is now different. Larger scores include 102, 103, 104, 105, 106, 107, 108 and 109. There are 8 of them, so that likelihood is 0.8, instead of 0.2 for the last problem.

    The method's the same, can you try it with the different numbers?
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