Question

If the time-dependent probability mass functions p N (t) (i.e., the probability that the population is of size N at time t) satisfy the differential equations dtdp N (t) =b[(N−1)p N−1 (t)−Np N (t)],N=1,2,…, and p N =0 for N

Answer 1

The given differential equations describe the time-dependent probability mass functions and their relationship to population size. They involve the per capita birth rate, death rate, and recursive relations for different population sizes.

Step-by-step explanation:

The given differential equations represent the time-dependent probability mass functions, which represent the probability that the population is of size N at a specific time t. The equation dt * dp N (t) = b * ((N-1) * p N-1 (t) - N * p N (t)) is a recursive relation that describes the change in probability over time for different population sizes. The coefficients b and d represent the per capita birth and death rates, respectively.