# Correlation of independent random processes

Suppose $$X(t)$$ and $$Y(t)$$ be two independent random processes. Is $$E(X(t_1)Y(t_2))$$ necessarily zero?

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• No. $E<X \cdot Y>$ is simply $E<X> \cdot E<Y>$ – Hilmar Jul 12 at 10:55

If $$X$$ and $$Y$$ are independent random variables, then the expectation operator $$\operatorname{E}$$ has the property
$$\operatorname{E}[X Y] = \operatorname{E}[X]\operatorname{E}[Y].$$
Consider your $$X(t_1)$$ and $$Y(t_2)$$ as $$X$$ and $$Y$$ in this answer. If both $$\operatorname{E}[X] \ne 0$$ and $$\operatorname{E}[X] \ne 0,$$ then the product $$\operatorname{E}[X]\operatorname{E}[Y]$$ will be non-zero.