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Homework Statement
Suppose that X has pdf
f(x) = k[itex]x^{2}[/itex] for -1[itex]\leq x \leq 1[/itex], 0 otherwise
(a) What is k?
(b) What is E[itex]x^{n}[/itex] where n[itex]\geq 0[/itex] is an odd integer?
(c) What is E[itex]x^{n}[/itex] where n[itex]\geq 0[/itex] is an even integer?
Homework Equations
The Attempt at a Solution
For (a) I get 1.5
For (b) I get (-3/8)
for (c) I get (9/8)
C is my concern because the expected value for when n is even is greater than one. Is this a problem? My initial thought that it was because x takes on values greater than 1 and have a probability of occurring. I have checked my work and saw nothing wrong. So I just wanted to make sure that my answer to c was impossible before posting my math. It's very simple math and I don't see what I'm doing wrong. Thanks for any help that you can provide.