Question 1: Compute the page rank for each of the pages below. Assume =0. Stop after 4 iterations.

Question 2: We want to estimate the size of the vocabulary for a corpus of 1,000,000 words. However, we only know statistics computed on a smaller corpus:

For 500,000 words, there are 150,000 unique words

We are also given the value of B=0.5.

Estimate the vocabulary size for the 1,000,000 words corpus

How about for a corpus of 1,000,000,000 words?

Question 3: Suppose that you are attempting to improve a web search engine, and are investigating the use of anchor text in search. For each web page indexed by your search engine, you find the set of anchor text phrases in all the hyperlinks to that page. What methods might you use to determine which items in that set are the best descriptions of the content of the page? Give examples of anchor text phrases that are likely to be frequent in anchor text but useless for your purpose?