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Random variable, expected value,Variance

  1. Oct 16, 2011 #1
    Hi.
    I choose randomly a one word, and I decided to choose a word blue. Let random variable x be a length of the word blue. What is expected value and variance of a word blue?



    So, random variable x = 4.

    E(X) = Ʃ xi fX(xi)
    i:xi∈S

    x1 + x2 + x3 + x4 = 10.

    expected value = 10.


    Variance is

    Var(X) = E[X − E(X)]^2


    Var(X) = E[10 − E(4)]^2 = 6^2 = 36


    Variance = 36
     
  2. jcsd
  3. Oct 17, 2011 #2
    I do a little improvement.

    E(X) = Ʃ xi f(x)p(x)
    i:p(x)∈S

    x1 + x2 + x3 + x4 = 10.

    expected value = 10. Is this correct?


    Variance is

    Var(X) = E[X − E(X)]^2


    Var(X) = E[10 − E(4)]^2 = 6^2 = 36


    Variance = 36. Is this correct?
     
  4. Oct 17, 2011 #3

    mathman

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    The problem as described has a mean of 4 (blue has 4 letters) and a variance of 0 (blue has 4 letters - no variation).
     
  5. Oct 18, 2011 #4
    Can you formalize those solutions?

    I don't understand.
    Do you mean that expected value is 4 ? Mean = expected value?

    And because blue has 4 letters - no variation. so variance is

    Var(X) = E[4 − E(4)]^2 = 0 ??
     
  6. Oct 18, 2011 #5

    mathman

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    Science Advisor
    Gold Member

    Mean = expected value (almost by definition - since mean may be defined as sample mean or true mean - the expected value).

    Var(X) = 0, as you described.
     
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