The capacity of a Binary Symmetric Channel (BSC) with cross - over probability 0.5 is ______ .

A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this first 'Head'. The entropy H (L) in bits is _______________.

The forward path transfer function of a unity negative feedback system is given by $$$G\left(s\right)\;=\;\frac k{\left(s\;+\;2\right)\left(s\;-\;1\right)}$$$ The value of K which will place both the poles of the closed-loop system at the same location, is ______.

For the following feedback system $$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of the step response is required to be less than 2 seconds. Which one of the following compensators C(s) achieves this?