7.5 Prove Eq. 7.22. h(x) = j=0 (j)xj = j=0 xj k1=0 km=0 (j, i ki) m i=1 p(i)

7.5 Prove Eq. 7.22. h(x) = ∞ j=0 π(j)xj = ∞ j=0 xj ∞ k1=0 ··· ∞ km=0 δ(j,  i ki) m i=1 p(i) ki = m i=1 Pi (x); where Pi (x) = ∞ k=0 p(i) k xk . The probability π(j) was π(j) = ∞ k1=0 ··· ∞ km=0 δ  j,  i ki m i=1 p(i) ki