  In this work we consider random Boolean networks that provide a general model
for genetic regulatory networks. We extend the analysis of James Lynch who was
able to proof Kauffman's conjecture that in the ordered phase of random
networks, the number of ineffective and freezing gates is large, where as in
the disordered phase their number is small. Lynch proved the conjecture only
for networks with connectivity two and non-uniform probabilities for the
Boolean functions. We show how to apply the proof to networks with arbitrary
connectivity $K$ and to random networks with biased Boolean functions. It turns
out that in these cases Lynch's parameter $\lambda$ is equivalent to the
expectation of average sensitivity of the Boolean functions used to construct
the network. Hence we can apply a known theorem for the expectation of the
average sensitivity. In order to prove the results for networks with biased
functions, we deduct the expectation of the average sensitivity when only
functions with specific connectivity and specific bias are chosen at random.
