Arnold F. answered • 02/22/16
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Are you asking for [E(x)]3 or E(x3) ?
Arnold F.
E(x3) is the easy one. By symmetry of the standard normal around zero that expected value is 0; the + and - "values" have the same "density values" so they would cancel out.
E(x4) I will have to check out myself.
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02/23/16
Sasha D.
Thank you, let me know how that goes!
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02/23/16
Arnold F.
Here's what I've got:
For a standard normal distribution z, x=z2 is a chi-squared distribution with one degree of freedom. So E(x)=1 (# degrees of freedom) and Var(x)=2 (i.e.2 x df)
Var(x) = E(x2) - [E(x)]2 = E(z4) - [E(z2)]2
2 = E(z4) - 1
So it my work here is correct E(z4) = 3
Have you had chi-squared dist yet?
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02/23/16
Sasha D.
no we have not!
Its gives the hint integration of x2e−x2/2 by parts, u = x^2e^−x2/2, v = x
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02/23/16
Arnold F.
Sasha,
Do you still need a solution here?
I have not tried using the hint yet but it might require integration by parts 2 or 3 times.
Arnold
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02/24/16
Sasha D.
02/22/16