Let y0, y1, y2,... be a sequence of random unsigned 32 bit integers
(i.e. 0 yi 232, every value equally likely).
For the sequence xi the following recursion is given:
It can be seen that eventually there will be an index N such that xi = 232 -1 (a bit-pattern of all ones) for all i N.
Find the expected value of N.
Give your answer rounded to 10 digits after the decimal point.