# Simple question about expected value

by pamparana
Tags: expected, simple
 P: 109 Hello, 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, Luc
 P: 608 I suppose the probability space is $[0,2 \pi)$ 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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