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Math Help - Statistics - Bernoulli and related variables (Berry & Lindgren Book)

  1. #1
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    Statistics - Bernoulli and related variables (Berry & Lindgren Book)

    Review Problem, 4-R2 in Berry & Lindgren - Statistics: Theory & Methods



    Let X ~ Ber(.04). If this experiment is repeated in independent trials.

    (a) how many trials, on average, would be required to get six successes?

    Let X1 denote the number of successes in 50 trials and X2, the number of successes in 50 additional trials. Let Y = X1 + X2.


    (b) Find the mean and variance of Y.

    (c) Give the distribution of Y (name and parameter value)

    (d) Find P(Y<=5) (that's Y equal to or smaller than 5)

    (e) Find the probability that if there are six successes in the 100 trials, these are evenly divided between the first 50 and the second 50 trials.



    That's it.
    Any help is sincerely appreciated.

    Thanks, Simon DK.
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  2. #2
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    Okay, so the answer for the first two questions are...

    A:

    E(Q) = n * p , where n are number of trials and p is probability...

    When n is unknown and E(Q) is 6 and p is 0,04, then

    n = 6/0,04 = 150.


    B:

    X1 = 50 and X2 = 50, so Y = x1 + x2 = 100, so n = 100.

    Var(Y) = n * p * q , where n are number of trials, p is probability and q is (1 - p)

    Var(Y) = 100 * 0,04 (1 - 0,04) = 3,84.


    and

    E(Y) = n * p = 100 * 0,04 = 4.



    I'm however still having trouble with the next questions...
    I tried to put up a binomial distribution two answer C, but as the answer is supposed to be 0.785, it doesn't match my answer of 0,78837. So it is probably wrong... Any ideas?

    Follow-up:
    The answer is...

    P(Y<=5) = SUM from k = 0 to 5 of ( (100*0,04)^k / k! ) * exp(-100*0,04) = 0,78513.


    and the answer for the last question is .322..?
    Last edited by sh01by; November 15th 2007 at 07:22 PM. Reason: about the last question...
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