E[x^n] when n is odd as opposed to when it's even

Allie Z

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Oct 12, 2018
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Let X be a random variable with N(0,1) distribution. Show that E[X^n] = 0 if n is odd, and (n-1)(n-3)...3 x 1 if n is even. What are some ways to approach this?
 
Let X be a random variable with N(0,1) distribution. Show that E[X^n] = 0 if n is odd, and (n-1)(n-3)...3 x 1 if n is even. What are some ways to approach this?

1) Definition
2) Symmetry

What are your thoughts?
 
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