Problem $4.$ Find the entropy and the binary Huffman code for the random variable $x$ with pmf

$p_x(x)=\{\begin{array}{ccc}\frac{x}{21},& x=1,2,\text{d}\text{o}\text{t}\text{s}\text{,}& 6,\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}\text{.}& \end{array}$

Also calculate $E[l(x)]$ when Huffman code is used.