#2. Expected Length of Coding Scheme (6 points) Suppose that several information sources generate symbols at random from a five-letter alphabet (A, B, C, D, E) with different probabilities. We will try different encoding schemes for encoding these symbols in binary. Given the probabilities and an encoding scheme, you will compute the expected length of the encoding of n letters generated by the information source. You may use any rigorous method of analysis you like, but must show your work and justify your answer. (a) (2 pts) Suppose that the symbols occur with probabilities Pr[A]-0.3, PrB]-03, Pric] = 0.2. Pr[D] 0.1, and Pr[E] 0.1, and the coding scheme encodes these symbols into binary codes as follows: A 001 010 011 D 100 E 101 What is the expected length of the encoding for these probabilities and encoding? (b) (2 pts) Now suppose that the symbols occur with the same probabilities Pr[A]-0.3, Pr[B]- 0.3, Pr[C] 0.2, Pr[D]0.1, and Pr[E]0.1, but we have a different encoding scheme: A 0 B 10 110 D 1110