Find average codeword length for the huffman code

Question

Solve the following problem:

A discrete memory less source is described by the alphabet X = {x₁, x₂,..., x₈}, and the corresponding probability vector p = {0.2, 0.12, 0.06, 0.15, 0.07, 0.1, 0.13, 0.17}.

Design a Huffman code for this source; find L, the average codeword length for the Huffman code; and determine the efficiency of the code defined as

η = H(X)/L¯