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Expected value of the area of square

  1. Apr 24, 2007 #1
    1. The problem statement, all variables and given/known data
    Given a square with side lengths X, where X is a random variable with some probability density function (the actual pdf is not important for my question). Why isn't the expected value of the area = E[X]^2 = E[X^2]?


    2. Relevant equations



    3. The attempt at a solution
    Intuitively I would think, if I can find the expected value of one of the sides, I can get the expected value of the area by squaring it.
    On the other hand, I am well aware that E[X]^2 != E[X^2] in the general case, and this is indeed a general case (with some geometric interpretation).
     
  2. jcsd
  3. Apr 24, 2007 #2
    Wait nevermind, I got it.
     
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