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?
x(t) = U + Vt.
Where U is a zero mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is _________________