3.2. Collards were planted equally spaced in a single row in order to provide an experimental setup for observing the chaotic movements of the flea beetle (P. cruciferae). A beetle at position k in the row remains on that plant for a random length of time having mean mk (which varies with the

"quality" of the plant) and then is equally likely to move right (k + 1) or left (k - 1). Model the position of the beetle at time t as a birth and death process having parameters Ak = μk = 1/(2mk) for k = 1, 2, ... , N - 1, where the plants are numbered 0, 1, . . . , N. What assumptions might be plausible at the ends 0 and N?