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?
Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x), as shown in the figure.
Consider a 1 bit quantizer that maps positive samples to value $$\alpha$$ and others to value $$\beta$$. If $$\alpha$$* and $$\beta$$* are the respective choices for $$\alpha$$ and $$\beta$$ that minimize the mean square quantization error, then ($$\alpha$$* $$-$$ $$\beta$$*) = ___________ (rounded off to two decimal places).
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 _________________