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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 ≥ 1}are i.i.d. random variables with the same distribution as X(1).
(a) What is the expected number of individuals in generation 1?
(b) Find the generating function of the number of individuals in genera- tions 1 and 2, respectively.
(c) Determine/express the probability that the population is extinct after two generations.
Remark. It may be helpful to let p0 denote the probability that an in- dividual does not have any children (which, in particular, means that P (X(1) = 0) = p0).
Create the acceptance-rejection technique for creating the geometric random variable, X, with parameter p on range {0, 1, 2, ...}.
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Let G be a directed graph where c_e is the cost of arc e. If the nodes of G can be assigned feasible potentials then G has no negative dicycle.
Can you tell me what are the advantages and limitations of applying nonparametric tests in solving business problems?
What is the probability that the diameter of a single randomly chosen axle differs from the target value by 0.01 mm or more?
A basketball team has sixteen women on the roster. In how many ways can the coach choose a roster consisting of five different positions?
In a particular region of Rhode Island, it is known that fisherman's trap on average of 32 pounds of lobster per day with a standard deviation of four pounds.
question to estimate the prevalence of hiv the state of new york implemented a policy of testing women who gave birth.
A chance sample of 50 families revealed an average or median of $112,000 and a standard deviation of $40,000. What is the standard error of the average or median?
What is the natural model for design and how many d.f. are there for each term in the model - design while the design was still being created.)
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