Consider the zero$-$memory source with probabilities $\{0\mathrm{.}4,0\mathrm{.}2,0\mathrm{.}1,0\mathrm{.}1,0\mathrm{.}1,0\mathrm{.}05,0\mathrm{.}05).$

a$).$ Construct a binary Huffman code by placing the composite symbols as low as possible.

b$).$ Construct a binary Huffman code by placing the composite symbols as high as possible.

In each case compute the variances of the word length and comment on the result.