The PDF of a Gaussian random variable X is given by $${p_x}(x) = \,{1 \over {3\sqrt {2\pi } }}\,\exp \,[ - \,{(x - 4)^2}/18]$$.

The probability of the event {X = 4} is

A feedback control system is shown in figure (a) Draw the signal-flow graph that represents the system.
(b) Find the total number of loops in the graph and determine the loop-gains of all the loops.
(c) Find the number of all possible combination of non-touching loops taken two at a time.
(d) Determine the transfer function of the system using the signal-flow graph.

If the characteristic equation of a closed-loop system is s² + 2s + 2 =0, then the system is

The equivalent of the block diagram in Figure is given as