5. A random process known as the random amplitude sinusoid is defined as $X[n] = A \cos(2\pi f_0 n)$ for $-\infty < n < \infty$ and $A \sim \mathcal{N}(0, 1)$. Find the mean and covariance sequences. Then, plot some realizations of $X[n]$ in an overlaid fashion.
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The mean of a random variable is defined as E[X] = ∫ x f(x) dx, where f(x) is the probability density function of X. In this case, X[n] = A cos(2πfn) and A ~ N(0,1). Since A is a random variable with a standard normal distribution, its mean is 0. Therefore, the Show more…
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