How I approach the following continuous time random process question? $W$ has a constant PSD, so it is white noise. So, $X$ is a normally distributed RV, and $Y$ is a normally distributed RV with the same mean as $X$ and 2 times its variance, I believe. To answer the question fully, I would need to compute the mean and variance of $X$ and $Y$ and apply the formula for the correlation coefficient. But, how do I compute these parameters, as well as the expected value of the product of $X$ and $Y$ , i.e. $E(XY)$ ? Problem: Let $W(t)$ be white Gaussian noise with (constant) PSD $S_W(f)$ = 1. Let $g(t)$ and $h(t)$ be the rectangular pulses of height 1 with durations 1 and 2, respectively, both starting at time zero. Define the random variables $X$ and $Y$ according to: $$X = \int_{- \infty}^{\infty} g(t)W(t) \ dt $$ $$Y = \int_{- \infty}^{\infty} h(t)W(t) \ dt $$ What is the correlation coefficient between $X$ and $Y$ ?

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