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Simple statistics expectation calculation

  1. Nov 2, 2012 #1
    1. The problem statement, all variables and given/known data

    I am just trying to figure out how to calculate the expectation of something.
    The context is for a random sample from a normal distribution with known mean μ and unknown variance σ2.

    2. Relevant equations



    3. The solution

    So for the purposes of this question we set θ = σ2
    I want to calculate:

    -E(n/2θ2 - [itex]\sum[/itex](xi-μ)/2θ3)

    The answer ends up being just n/2θ2
    Why is the second term 0?

    Also if anyone has any links or notes about expectation of values similar this, for example, that would be great.
    Thanks
     
  2. jcsd
  3. Nov 2, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    What are the values of E(X1-μ), E(X2 - μ), etc.?

    BTW: it is customary in Probability discussions to use a capital letter to stand for a random variable and the corresponding small letter to stand for a possible value; so x is a possible value of the random variable X, and you are sampling from a multi-dimensional random variable (X1, X2, ... Xn). Talking about E(X-μ) is different from talking about E(x-μ): one of them is the expectation of a random variable, while the other is the expectation of a non-random number (which of course, is just that number itself).

    RGV
     
  4. Nov 3, 2012 #3
    It would be
    Ʃ (E(Xi) - μ) = 0
    ?

    How would I calculate E(1/2θ3) ? (I know I wouldn't need to here since it's 0 on top, but just out of curiosity)
     
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