I am reading this paper on how information is propagated on the Bitcoin network. The authors present a model to predict the rate at which forks occur in the blockchain which is given as below Here, F is the number of conflicting blocks in the network, Pb is the probability of the network finding a block b in a given second (ideally, 1/600 since a block is expected every 10 mins = 600 secs) and f(t) represents the ratio of nodes that hear about the block b in t secs. However, what I cannot understand is how this entire expression is derived. I understand that the term in the exponent represents the mean amount of time it takes for the network to learn about a block (and this value can be derived from a graph given in the paper). I assume 1 - Pb represents the probability of the network finding more blocks in the remaining 599 seconds in the 10-minute interval. Why is this probability raised to the mean amount of time it takes for the network to learn about a block?
Any explanation would be appreciated.