Branching process with reproduction mean

Reference no: EM13985345

1. Consider a branching process with reproduction mean m 1. Suppose also, as before, that X(0) = 1.

(a) What is the probability of extinction?

(b) Determine the expected value of the total progeny.

2. The following model can be used to describe the number of women (mothers and daughters) in a given area. The number of mothers is a random variable X ∈ Po(λ). Independently of the others, every mother gives birth to a Po(µ)-distributed number of daughters. Let Y be the total number of daughters and hence Z = X + Y be the total number of women in the area.

(a) Find the generating function of Z.

(b) Compute E Z and Var Z.

Reference no: EM13985345

Questions Cloud

Perform exploratory data analysis on creativitypre : Create two graphs-one for systolic and one for diastolic pressure. Each graph should clearly delineate the three groups - Perform exploratory data analysis on both the SystolicBP and DiastolicBP variables.

Determine the generating function : Consider a branching process with a Po(m)-distributed offspring. Let X(1) and X(2) be the number of individuals in generations 1 and 2, respectively. Determine the generating function of

Generation of a branching process : Let X(n) be the number of individuals in the nth generation of a branching process (X(0) = 1), and set Tn = 1 + X(1)+ · · · + X(n), that is, Tn equals the total progeny up to and including generation number n.

Compute direction of electric field inside velocity selector : From the information above, determine the direction of the electric field inside the velocity selector.(indicate it on the diagram).

Branching process with reproduction mean : 1. Consider a branching process with reproduction mean m 1. Suppose also, as before, that X(0) = 1.

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

User Account

All Pages