Generating function of the number of individuals

Reference no: EM13985340

Consider the following modification of a branching process: A mature individual produces children according to the generating function g(t). However, an individual becomes mature with probability α and dies before maturity with probability 1 - α. Throughout X(0) = 1, that is, we start with one immature individual.

(a) Find the generating function of the number of individuals in the first two generations.

(b) Suppose that the offspring distribution is geometric with parameter p. Determine the extinction probability.

Reference no: EM13985340

Questions Cloud

How has the patient been affected by the changes : Consider the following questions as you write your article: What has changed over the last 20 years? Have the changes been positive or negative? How has the patient been affected by the changes

Determine the mass of the atom : From the information above, The electric field strength in the selector is 4.819 x 105 N/C. The atom passes straight through the selector without any deflection of its path. Determine the mass of the atom.

Problem regarding the galton-watson process : Let {X(n), n ≥ 0} be the usual Galton-Watson process, starting with X(0) = 1. Suppose, in addition, that immigration is allowed in the sense that in addition to the children born in generation n there are Zn indi- viduals immigrating, where {Zn, n ≥ ..

Design a tri-gneration system on aspen hysys : Design a tri-gneration system on ASPEN HYSYS - find the answers have to be shown power output from fuel cell and engine efficiency

Generating function of the number of individuals : (a) Find the generating function of the number of individuals in the first two generations. (b) Suppose that the offspring distribution is geometric with parameter p. Determine the extinction probability.

Define michelle objectives and opening bids : Define the resistance points. Define Michelle's alternatives and select a BATNA. Define Michelle's objectives (targets) and opening bids (where to start)

Find the distribution of y : (a) Find the distribution of Y. (b) Determine the probability of extinction.

What is the average induced emf : A 5.4 cm diameter circular loop of wire is in a 0.72 T magnetic field. The loop is removed from the field in 0.29 s . Assume that the loop is perpendicular to the magnetic field. Part A What is the average induced emf? Express your answer using tw..

Determine the value of the potential difference : From the information above, determine the value of the potential difference through which the atom was accelerated.

User Account

All Pages