A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$,
when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t = t_k$, the variance of the random variable $n(t_k)$ is ________.
For a real signal, which of the following is/are valid power spectral density/densities?
The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure.
Statement I : The system is necessarily a pure delay system for inputs which are bandlimited to $$-$$$$\alpha$$ $$\le$$ f $$\le$$ $$\alpha$$.
Statement II : For any wide-sense stationary input process with power spectral density SX(f), the output power spectral density SY(f) obeys SY(f) = SX(f) for $$-$$$$\alpha$$ $$\le$$ f $$\le$$ $$\alpha$$.
Which one of the following combinations is true?
The autocorrelation function $R_X(\tau)$ of a wide-sense stationary random process $X(t)$ is shown in the figure.
$$ \text { The average power of } X(t) \text { is ___________} $$
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