Please see the problem in the attachment.

A search engine is looking for a particular document. Any given website carries a copy of the document with probability p independently of others. The engine spends a random amount of time, that is exponentially distributed with parameter A, searching for a copy of the document in a given website until either the document is found and then the search is stopped or the document is not found and the next website is visited. Assume that the websites are listed as 1, 2,3, . . ., all the way to innity (a reasonable model for the internet which has around 1 billion websites), and let U,- denote the time spent on website i. Let V denote the time spent by the engine to nd a copy of the document. Observe that V 2 U1 | U2 + . . . -|- UN, U,- N exp()\\), and N is a geometric random variable with parameter p, and U1, U2, . . ., are mutually independent. Using MGF, nd the PDF of V