Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below.

The optimum threshold to achieve minimum bit error rate (BER) is

Let U and V be two independent zero mean Gaussian random variables of variances $${{1 \over 4}}$$ and $${{1 \over 9}}$$ respectively. The probability $$P(\,3V\, \ge \,\,2U)$$ is

The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$$, when connected in feedback as shown below, the approximate value of K_a that will reduce the time constant of the closed-loop system by one hundred times as compared to that of the open-loop system is

The signal flow graph for a system is given below. The transfer function $$\frac{Y(s)}{U(s)}$$ for this system is