M = { { -(n lambda), mu } ,{ n lambda, -(mu + n-1 lambda) } } VarM = { { S + (n lambda), mu } ,{ n lambda, S + (mu + n-1 lambda) } } OneMatrix = {1,1} VarOneMatrix = {{1},{1}} Prob = {{1},{0}} VarProb = {1,0} SecondMoment = (Limit[(-2 VarProb . (D[(Inverse[VarM]),S])),S->0]) . VarOneMatrix MTTDL = Simplify[- OneMatrix . Inverse[M] . Prob] Variance = Simplify[SecondMoment - MTTDL^2]