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Homework Help: Bernoulli variance

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

    Show how Var(Xi) depends on p writing it as a function [tex]\sigma[/tex]^2(p)

    3. The attempt at a solution

    Var[Xi] = E[Xi^2] - E^2[Xi] = p-p^2 = p(1-p)

    not sure where to go from here to get it in the form [tex]\sigma^2[/tex](p) ?
  2. jcsd
  3. Aug 1, 2010 #2


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    Science Advisor

    Please clarify you question. In particular, what is "p"? The mean?

    If I understand the rest, The standard deviation, [itex]\sigma[/itex] is defined as the square root of the variance. The variance is [itex]\sigma^2[/itex].
  4. Aug 1, 2010 #3
    p in this case is the probability of success. Xi is a Bernoulli random variable.

    This is a standard Bernoulli question but I just dont understand what the question is asking when it says "writing it as a function sigma^2(p)". Does that mean calculate the variance of the probability? Surely not. In which case it must just be p(1-p)?
  5. Aug 1, 2010 #4


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    Homework Helper

    think about common function notation: when you write a function of [tex] x [/tex] you use [tex] f(x) [/tex]. Since the variance in the binomial setting is a function of [tex] p [/tex], the corresponding way to write it is [tex] \sigma^2(p) [/tex] - variance as a function of [tex] p [/tex]. It looks awkward, but you're stuck with it.
  6. Aug 1, 2010 #5
    I see. That makes sense. Thanks
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