3 Efficient Encoding (30 pts) An information source generates symbols at random from a four-letter alphabet {a,b,c,d} with probabilities Pr[a] = 1/2, Pr[b] = 1/4, Pr[c] = 1/8, Pr[d= 1/8. A coding scheme encodes these symbols into binary codes as follows: a: 0 b: 10 c: 110 d: 111 Compute the expected length of the encoding of n letters generated by the information source. You may use any method you like, but must show your work/justify your