Galton-Watson Process, help needed! thanks all!

Q1 Let (X_n) for n>0 be a Galton-Watson branching process starting with one particle (that is, X_0 = 1) and offspring distribution

p0 = 1/6 ; p1 = 1/3 ; p2 = 1/3 ; p3 = 1/6 ;

(A) P[lim n->infinity, X_n = 0] > 0
(B) P[lim n->infinity, Xn = infinity] > 0
(C) EX_n < EX_n-1
(D) P[Popul. ever dies out] = 0.5*sqrt(13) - (3/2)
(E) E(X_10) approx= 62:125
(F) Var(X_10) approx= 128.831...



Q2 Let (X_n), for n>0 be a Galton-Watson branching process starting with one particle (that is, X_0 = 1) and offspring distribution

p_k =(lamda^k)*exp(-lamda)/ (k!) ; k >= 0; 0 < k < 1;

(A) P[lim n->infinity, X_n = 0] < 1
(B) P[lim n->infinity, Xn = infinity] = 0
(C) EX_n < EX_n-1
(D) 0 is transient
(E) E(Xn) = lamda^n
(F) Var(Xn) = (lamda^n)*(sigma^2)


Thank you soo much!

We certainly get the gamut of questions here, from cheating boyfriends to Galton-Watson branching processes. To be honest with you, I don't know what that is. Hopefully ME or CM can be of more help.

Is this True/False or do you pick an answer A to F? Some of the statements in A-F are clearly wrong given the info stated in Q1.

The Galton–Watson process is a branching stochastic process arising from Francis Galton's statistical investigation of the extinction of family names.

Quote: CrystalMath

Is this True/False or do you pick an answer A to F? Some of the statements in A-F are clearly wrong given the info stated in Q1.

pick an answer from A to F

Q1 Let (X_n) for n>0 be a Galton-Watson branching process starting with one particle (that is, X_0 = 1) and o ffspring distribution

p0 = 1/6 ; p1 = 1/3 ; p2 = 1/3 ; p3 = 1/6 ;

(A) P[lim n->infinity, X_n = 0] > 0
(B) P[lim n->infinity, Xn = infinity] > 0
(C) EX_n < EX_n-1
(D) P[Popul. ever dies out] = 0.5*sqrt(13) - (3/2)
(E) E(X_10) approx= 62:125
(F) Var(X_10) approx= 128.831...

C is false, since EX_n = EX_n-1 * 1.5 .
E is false, since EX_10 = 1.5^10 = 57.665 .

Tell us what you know, and maybe we can help more.