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Distribution of Bernoulli random variable

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data

    a) Let X1, X2, ...XN be a collection of independent Bernoulli random variables. What is the distribution of Y = [itex]\sum[/itex]Ni = 1 Xi


    b) Show E(Y) = np

    2. Relevant equations

    Bernoulli equations f(x) = px(1-p)1-x

    3. The attempt at a solution

    a)X1 + X2 + .... + XN = p

    b) Not sure. I'm assuming the expectation would mean when each probability is multiplied by "x", the x's go from 0 to n, meaning they represent the n.
     
  2. jcsd
  3. Dec 9, 2011 #2

    LCKurtz

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    Have you stated the question carefully and correctly? What is p? Are the independent random variables of the same distribution? Have you studied binomial distributions yet?
     
  4. Dec 9, 2011 #3
    Yeah, I have studied the binomial. I'm going back and looking at old tests before my final, so I'm trying to remember the way the solution worked.

    I was easily able to derive the mean and variance from a Bernoulli distribution, but I'm having trouble with these two problems.

    Also, p is the expected outcome. I'm assuming you're just deriving the mean of the Binomial distribution here, but I'm not sure how that is done.
     
  5. Dec 9, 2011 #4

    LCKurtz

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