LetXbe a random integer number from 0 to 2^d 1. Denote byM(X)the length 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.

Part A: Show a lower bound onE[M(X)]

Part B: Show an upper bound onE[M(X)]

Ideally, the upper and lower bounds should be within a constant factor from each other: f(d) <= E[M(X)] <= c*f(d)