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

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?