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We wish to estimate the surprise number ( 2 nd moment ) of a data stream, using the method of AMS. It happens that our

We wish to estimate the surprise number (2nd moment) of a data stream, using the method of
AMS. It happens that our stream consists of ten different values, which we'll call 1,2,dots,10, that
cycle repeatedly. That is, at timestamps 1 through 10, the element of the stream equals the
timestamp, at timestamps 11 through 20, the element is the timestamp minus 10, and so on. It
is now timestamp 75(it is the last timestamp in the stream), and a 5 has just been read from
the stream.
For our estimate of the surprise number, we shall choose three timestamps at random, and
estimate the surprise number from each, using the AMS approach (length of the stream times
2m-1, where m is the number of occurrences of the element of the stream at that timestamp,
considering all times from that timestamp on, to the current time 75). Then, our estimate will
be the median of the three resulting values.
Identify from the list below the set of three "random" timestamps that give the closest
estimate, and explain why.
a){24,44,65}
b){31,48,50}
c){37,46,55}
d){25,34,47}
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