Let $$\left( {{X_1},\,{X_2}} \right)$$ be independent random variables, $${X_1}$$ has mean 0 and variance 1, while $${X_2}$$ has mean 1 and variance 4. The mutual information I $$\left( {{X_1},\,{X_2}} \right)$$ between $${{X_1}}$$ and $${{X_2}}$$ in bits is ________________.

The open loop transfer function $$$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\mathrm p\left(\mathrm s\;+\;2\right)\left(\mathrm s\;+\;3\right)}$$$ Where p is an integer, is connected in unity feedback configuration as shown in figure. Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________.

Which one of the following options correctly describes the locations of the roots of the equation s⁴ + s² + 1 = 0 on the complex plane?

A linear time invariant (LTI) system with the transfer function $$$G\left(s\right)=\frac{K\left(s^2+2s+2\right)}{s^2-3s+2}$$$ is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < $$\infty$$ intersects the imaginary axis for K = 1.5. The closed loop system is stable for