A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal to quantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample needed to achieve the desired SQNR is ________ .

Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure. The channel is

Consider the random process
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 _________________

For the system shown in the figure, Y (s) / X (s) = __________.