Suppose the n$-$vector w$$ is the word count vector associated with a document and a dictionary of n words. For simplicity we will assume that all words in the document appear in the dictionary.

$($a$)$ What does $1$ w$$ convey?

$($b$)$ What does w$282=0$ mean?

$($c$)$ Let $$h be the n$-$vector that gives the histogram of the word counts, i$.$e$.,$ hi is the fraction of the words in the document that are word i$.$ Use vector notation to express $$h in terms of w$.($You may assume the document contains at least one word.$)$