where N ≥ ≥ 1 . The equation can be understood as simply the probability that an isoprene unit is NOT a cross-link (1− p x) in N −1 successive units along a chain. Since P (N) decreases with N, shorter chains are more probable than longer ones. Note that the number of statistically independent backbone segments is not the same as the number of isoprene units. For natural rubber networks, the Kuhn length contains about 2.2 isoprene units, so N ∼ ∼ 2.2 n . The product of equations (1) and (3) (the joint probability distribution) relates the network chain length ( N ) and end-to-end distance ( r ) between its terminating cross-link nodes: