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The Expectation of X and the Expectation of X squared (discrete math)

  1. Mar 3, 2009 #1
    1. The problem statement, all variables and given/known data
    prove or disprove that E[X^2] = E(X)^2

    2. Relevant equations
    E[X] = [tex]\sum[/tex]xi*pr(xi)


    3. The attempt at a solution

    I really don't know where to start, I believe that it is not true, so I should try to disprove it, and the easiest way to do that would be by counterexample... I don't understand expectation very well though, I could try to do a mathematical proof to show that they are not equal, but I don't know how to go about that either.
     
  2. jcsd
  3. Mar 3, 2009 #2

    lanedance

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    Homework Helper

    hi sammC - this is ripe for a counter example...

    easiest would be to try a distribution with only 2 outcomes, ie 50% probability of each occurring, then calculate E[x] and E[X^2]

    note E[X^2] = sum over i of pr(xi)*(xi^2)
     
  4. Mar 3, 2009 #3
    ah, this helps a bunch, thanks!
     
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