2. Let Z be a supercritical branching process with Zo = 1 and family-size generating function G. Assume that the probability n of extinction satisfies 0
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.42. 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 a and dies before maturity with probability 1-a. 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 extinetion probabilityConsider a branching process with generation sizes Zn satisfying Zo = 1 and P(Z₁ = 0) = 0. Pick two individuals at random (with replacement) from the nth generation and let L be the index of the generation which contains their most recent common ancestor. Show that P(L = r) = E(Z¹) - E(Z1) for 0 ≤r 0?
- b) A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by ye- f(y) = 0Show that the number Zn of individuals in the nth generation of a branching process satisfies P(Zn > N | Zm= 0) ≤ Gm (0) N for nSuppose you have a branching process with the following given probabilities that each individual in the current generation will, by the end of its lifetime, have produced j new offspring (j = 0, 1, 2, ...). Find the probability that each of these branching processes will eventually die out under the lassumption that X0 = 1. • PO = 14, P2 = 3 4. • PO = 14, P1 = 12, P2 = 14. • PO = 16, P1 =12, P3 = 13. • PO = 1 10 , P1 = 2 10 , P2 = 3 10 , P3 = 4 10A grasshopper hops between three flowers labeled 1, 2, 3. It starts from flower 1. Once it arrives at a flower, it sits there for a period of time distributed exponentially with parameter 2. Then it makes a jump, as follows: if it is located on flower 1, it jumps to 2 or 3 with equal probability; if it is located at 2, it jumps to 3, and if it is at 3, it jumps to 2. (a) Model the grasshopper using a continuous-time Markov chain. Find the states, the initial distribution, and the jump rates! (b) What is the probability that at time t the grasshopper will sit on the third flower?If a random variable X has the moment generating function Mx (t)= 2 - ť Determine the variance of X.3Give me right solution according to the question... Urgent pleaseM9Suppose that Y₁ = 0.5, Y₂ = 0.2, Y4 = 0.7 and Y5 = 0.6, represents a random sample. Each of these Y's comes from the same population and has as a density of fy, (vi) = (0+1)yi; 0 -1 It can be shown that the natural logarithm of the likelihood function is equal to: n* ln(0 + 1) + 0 *Σln(yi) a. Determine the form of the maximum likelihood estimator for 0. b. Use the MLE formula and the data provided to find an estimate for 0. = 0.6, Y3SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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