Suppose dots and dashes are transmitted over a telegraph line so that dots occur a fraction p of the time (where 0 < p < 1) and dashes occur a fraction 1 - p of the time. The information content of the telegraph line is given by I(p), where I(p) = -p In p (1 - p) ln(1 - p). -

(a) Show that I' (p) = -ln p + ln(1 - p).

(b) Set I'(p) = 0 and find the value of p that maximizes the information content.