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Rewriting the fourth moment in terms of

  1. Oct 16, 2011 #1
    rewriting the fourth moment in terms of....

    1. The problem statement, all variables and given/known data
    X is a random variable with moments E[X], E[X^2], E[X^3]. Suppose var(X)= σ^2, and that skewness is given as, S=[E(X-μ)^3)]/(σ^3) Rewrite the right hand side of the expression(see below) in terms of μ, σ^2, S and μ4

    2. Relevant equations

    E[X-μ]^4 = E(X^4) - 4[E(X)][E(X^3)] + 6[E(X)]^2[E(X^2)] - 3[E(X)]^4


    3. The attempt at a solution
    E[(X^4)] = μ, thats all I've got.
    I've been coming back to this all day and I can't see where σ^2, S and μ4 fit into the right side of the equation. Can anyone please give me an idea? Thanks.
     
  2. jcsd
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