Please solve it step by step and by explaining.

$3-$ The symbols $\{a,b,c,d,e,f,g,h\}$ are being transmitted from the communication

source with following probabilities: $\{\frac{1}{8},\frac{1}{16},\frac{1}{8},\frac{1}{32},\frac{1}{8},\frac{1}{4},\frac{1}{32},\frac{1}{4}\}$ respectively. Then,

calculate the followings:

a$)$ The entropy of this communication source $(25$ p$)$

b$)$ Explain the condition of maximum entropy and for this case, calculate the

maximum entropy $(25$ p$)$