A discrete memoryless source emits the symbols a, b, c with probabilities 0.1, 0.4, 0.5 respec-

tively.

(a) Find the expected length of the best one-to-variable prefix-free code for this source.

(b) Find the normalized expected length of the best two-to-variable prefix-free code for this

source.

(c) Is it true that for any discrete memoryless source, the two-to-variable prefix free code has

normalized expected length that is no worse than that of the best one-to-variable code?