6.2.1

Solution

a)

b)

c)

Q 6.3.4

Solution

a-b)

  • Therefore, the maximun value occured at \(X_n = 0.1\) m is \(C_n =0.0242\) for non-normalized distribution pdf.

Q 6.5.5

Solution

a-b-c)

  • The time to extinction diffusion stochastic/determinstic logistic pdf distribution have the same location of peaks with same shapes for three cases of limiting \(P_n = L = 10^{-8}\) , \(P_n = L = 10^{-4}\), and \(P_n = L = 10^{-2}\). However their pdf distribution scales are different. Their differences in scales of pdf distribution is due to the sentivitity dependence of limiting \(P_n = L\).

Q 7.4.3

Soluton

a-b-c

Q 8.2.4

Solution

Q 8.2.5

Solution

Q 8.4.5

Solution

a)

b)

Hence the discrete version and continous version of stochastic logistic Model will have the same mean and variance of \(P\) provided that \(\Delta t\rightarrow 0\) .

c)

Stochastic Logistic Model is time-dependent mean and variance which follows Normal distribution:

d)

Since Stochastic Logistic Model is time-dependent mean and variance which follows Normal distribution, therefore, it is not possible to have analytic solution.