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Homework Help: Bernoulli random variable problem

  1. Apr 3, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose we want to estimate a binomial proportion, p. We take a sample of size n and count X successes.

    Consider a Bernoulli random variable, Y that is 1 with probability p and 0 otherwise. Show that the mean and variance of Y are p and p(1-p), respectively.

    2. Relevant equations

    3. The attempt at a solution
    Not too sure what to do here. I know that the mean is calculated by [tex]\Sigma[/tex]xf(x) and variance is E(X-mean)2
  2. jcsd
  3. Apr 3, 2010 #2


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    Homework Helper

    Well write out your sample space

    y 0 1

    For y=p, your probability is?

    and in any other case such as y=0, the probability is?

    Then you just use your definition E(Y)=∑all y y P(Y=y)
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