Anonymous asked in Science & MathematicsMathematics · 2 years ago

Please help. Variance of X. V(X)?

In a shooting workout, a basketball player will keep shooting until he makes 10. If the probability that he makes a shots 0.7, and X let be the total number of shots he will take, calculate. V(X)=?

2 Answers

  • nbsale
    Lv 6
    2 years ago
    Favorite Answer

    Let X = random variable = the number of shots it takes for him to make 10.

    First look at the probability that he makes 9 of 9+k shots, which is

    q(k) = (0.7^9)(0.3^k) C(9+k,9)

    Then P(X=10+k) = .7q(k).

    We have to do it this way, because X = 10-k means that he makes exactly 9 out of 9+k, then makes the next shot.

    Now add that up for k = 0 to some reasonably large number, and you get that

    E(X) = 14.28517 = 100/7

    V(X) = 6.12244898

    Screen print part of my Excel spreadsheet is shown below, based on about 50 shots.

    I don't have an exact expression for V, but it might be 6 6/49, which is correct to 10 decimal places. This is pushing Excel's limits, but i think it's a good bet that 6 6/49 is the exact answer.

    Attachment image
    • farlin2 years agoReport

      Correct! Answer. Thanks!

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  • Pope
    Lv 7
    2 years ago

    You may have gotten a bit trigger-happy with the Best Answer button. The answer you chose is correct though.

    You have defined a negative binomial distribution with the following parameters:

    p = 0.7

    r = 10

    V(X) = r(p - 1)/p²

    = 10(1 - 0.7)/0.7²

    = 3000/49

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