Given this algorithm

Initialize X $0$

for each stream update do

Flip a coin that is HEADS with probability $1/2^$X

if the coin is HEADS then

X $$ X $+1$

return Z $=(2^$X$)1$

Compute, with proof, E $[$Z$]$ and

Calculate Variance$[$Z$]$ by showing E$[2^2$C$]=(3/2)*$ m$^2+(3/2)*$ m $+1$