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Math Help - Help with negative binomial distributions

  1. #1
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    Help with negative binomial distributions

    One of the questions in my probability homework reads:

    X denotes a negative binomial random variable, with p = 0.6 Find P(X ≥ 3) for a) r = 2 and b) r = 4.

    According to my teacher, the answers are 0.1792 and 0.45568, respectively, but I can't for the life of me figure out how he got them. I tried finding P(X ≥ 3) by turning it into 1 - P(X ≤ 2) and then calculating p(2), p(1), and p(0), but I kept getting 0 for my answer, which obviously isn't correct.

    Can someone please help me solve this problem, or explain to me how I would go about solving it? I'm really confused.

    Thanks.
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  2. #2
    Super Member Random Variable's Avatar
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    Your approach is correct.

     P(X=0) = \binom{1}{1} 0.6^{2}0.4^{0} = 0.36

      P(X=1) = \binom{2}{1} 0.6^{2}0.4^{1} = 0.288

     P(X=2) = \binom{3}{1} 0.6^{2}0.4^{2} = 0.1728

     1 - 0.36-0.288-0.1728 = 0. 1792
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  3. #3
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    Quote Originally Posted by Random Variable View Post
    Your approach is correct.

     P(X=0) = \binom{1}{1} 0.6^{2}0.4^{0} = 0.36

     P(X=1) = \binom{2}{1} 0.6^{2}0.4^{1} = 0.288

     P(X=2) = \binom{3}{1} 0.6^{2}0.4^{2} = 0.1728

     1 - 0.36-0.288-0.1728 = 0. 1792
    Thanks so much, this helped a lot. But I'm still a little confused about where the 3 came from in the P(X=2) equation. For future reference, how would I know how to find the number that goes there (same for the numbers in the first bracket of P(X=1) and P(X=0)?

    Edit: I also don't understand part b. I don't understand which numbers go where. Can you please help me?
    Last edited by mintsharpie; March 25th 2010 at 04:56 PM.
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  4. #4
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    Quote Originally Posted by mintsharpie View Post
    Thanks so much, this helped a lot. But I'm still a little confused about where the 3 came from in the P(X=2) equation. For future reference, how would I know how to find the number that goes there (same for the numbers in the first bracket of P(X=1) and P(X=0)?

    Edit: I also don't understand part b. I don't understand which numbers go where. Can you please help me?
    I don't see what the problem can be here. Unless you have never seen the pmf for the negative binomial distribution, in which case you are advised to consult your textbook.

    The pmf is given here: Negative binomial distribution - Wikipedia, the free encyclopedia

    and all you do is substitute the given numbers into it. Where do you get stuck in doing this?
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    I don't see what the problem can be here. Unless you have never seen the pmf for the negative binomial distribution, in which case you are advised to consult your textbook.

    The pmf is given here: Negative binomial distribution - Wikipedia, the free encyclopedia

    and all you do is substitute the given numbers into it. Where do you get stuck in doing this?
    Thank you so much! I didn't understand what the pmf was before. Sorry for double-posting, I just wanted an answer. But you've helped me figure it out now, so thanks.
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