Question: LetXbe a random integer number from 0 to 2d 1. Denote byM(X)thelength of the maximum consecutive sequence of 1's in the binary representation ofX. FindE[M(X)]

LetXbe a random integer number from 0 to 2d 1. Denote byM(X)thelength of the maximum consecutive sequence of 1's in the binary representation ofX. FindE[M(X)] up to a constant multiplicative factor.Remark: For the binary number "1101110", we haveM(1101110) = 3; and for the binary number "11110110011", we haveM(11110110011) = 4.

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