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 , 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 infinity, and let Ui denote the time spent on website i. Let V denote the time spent by the engine to find a copy of the document. Observe that V = U1 + U2 + ... + UN, Ui ~ exp(), and N is a geometric random variable with parameter p, and U1, U2, ...are mutually independent. Find E(V ).