2 Variance of Morris Counter [35 points] Prove equation Var(Z) = m(m-1) 2 on slide 27.first compute E[Z"], and then to compute the variance you will subtract from the second moment the mean squared, i.e. Var[Z] = E[Z2] - EZ].Properties of Morris algorithm 1. The expectation of the variable Z=2Xm satisfies the following: E[Z]=m+1 Corollary: Morris algorithm outputs an unbiased estimator of m. l. The variance on is equal to Var[Z]=m(m-1)/2 Observation: No improvement in terms of concentration as m grows since Var(Z)/E(Z)2 is constant. 27