An AC mains line has frequency 50 Hz, and an amplitude of220V, to which a DC voltage of -20 volts is added, so that the voltage swings between -240 to +200 V. find: i) average value (2marks ii) mean-square value (3marks iii) root-mean-square value (1marks) b) Give signal interpretations for the following statistical averages i) X(t) (1mark) ii) [X(t)] (1mark) iii) X (t) (1mark) iv) var{X(t)} (1mark) c) For a signal z(t) = x(t) + y(t) give expression for : i) The self-power of x(t) and y(t) ii) The cross power of x(t) and y(t) d) Discuss the effects of noise on operation of electronic systems (6marks) The minimum usable signal in analog circuit applications is limited by externally and internally generated noise. The noise level sets a lower bound on the magnitude of a signal that can be amplified. .