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Math Help - Probability Distribution

  1. #1
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    Probability Distribution

    A box of 10 flashbulbs contains 3 defective bulbs. A random sample of 2 is selected and tested. Let X be the random variable associated with the number of defective bulbs in the sample.

    1. Find the probability distribution of X.
    2. Find the expected number of defective bulbs in a sample.



    The distribution I created is:


    xi 0 1 2
    pi 7/15 7/15 1/15


    0 defective is 7/10*6/9 = 7/15



    1 defective is 7/10*3/9 + 3/10*7/9 = 7/15





    2 defective is 3/10*2/9=7/15

    E(x) = 0*7/15 + 1*7/15 + 2*1/15 = 9/15=.6
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  2. #2
    MHF Contributor matheagle's Avatar
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    Re: Probability Distribution

    hypergeometric, where

    P(X=x)={{3\choose x}{7\choose 2-x}\over {10\choose 2}}

    The mean is the same as a binomial, np where n=2 and p=.3, giving you .6 quickly
    NOW the variance if the hyper isn't the same as a binomial but is is asymptotically equivalent.
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  3. #3
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    Re: Probability Distribution

    Terrific, but I have to specifically complete the table and solve E(x). Is my work correct?
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