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Simple question about expected value

by pamparana
Tags: expected, simple
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May3-10, 06:50 AM
P: 127

Just came across this that:

E[cos(t)sin(t)] = 0

the expected value of the product of cos(t)sin(t) is 0. However, I am unable to convince myself that is the case. Can anyone help me understand why this is so?

Many thanks,

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May3-10, 08:27 AM
P: 607
I suppose the probability space is [itex][0,2 \pi)[/itex] with normalized Lebesgue measure? In that case, what it means is
\frac{1}{2\pi}\int_0^{2\pi} \sin(t) \cos(t)\,dt = 0

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