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 answer.