Shannon metrics

$($a$)(5$ points$)$ What is the capacity of an additive white Gaussian noise channel with bandwidth $5$ kHz $,$ power spectral density flat at $0\mathrm{.}0001,$ and signal power constraint $150.$

$($b$)(5$ points$)$ Calculate the entropy in bits of the random variable $x$ with probability mass function $(\frac{1}{4},\frac{1}{8},\frac{1}{8},\frac{1}{8},\frac{1}{8},\frac{1}{16},\frac{1}{16},\frac{1}{16},\frac{1}{16}).$

$($c$)(5$ points$)$ Compare the expected codeword length of the Shannon code and the Huffman code for the source in the previous question.