Google "Moriss's Algorithm counting" so as to get an idea what this question is about.

?

Counting the Number of tokens in a stream It is trivial to see that if there are m tokens in the stream, then [logzm] many bits suffice to keep track ofthe number of tokens. Now consider the following randomized algorithm. Probabilistic Counting: LetX 0. 62 6 d) For this part, we consider an alternate (and somewhat more elegant) way of modifying the basic estimator to achieve better estimates. Suppose you modify the 1 (1+a)x , for some a > 0 given algorithm as follows - you increment X with probability (a = 1 in the above algorithm). What should the algorithm return now? Determine the value of a that you need to choose in order to find an estimate Y such that IY ml 5 em with probability at least 9/10? Disclaimer: The solution to the above problem can be found on the internet with a little effort. But I need an answer with good and legit explanation