Question related to branching processes. Zn is the number of offspring in generation n. I know that Pk is a geometric distribution, but am unsure of where to go from there.
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Question related to branching processes. Zn is the number of
offspring in generation n. I know...
Problem 2. Problem 1 doesn't need to be done, it's here for reference 166 Branching processes...
Problem 2. Problem 1 doesn't need to be done, it's here for
reference
166 Branching processes is a branching process whose .... is a branchin the result zes have mean μ (s l ) and variance σ 2, then var( ZnJun of Problem 9.6.1 to show that, if Zo. z 2. Use ditioning on the value of Zm, show th ose fa outition theorem and conditioning on the value of Z 9.6 Problems I. Let X1 , X2. . ....
2. Let(Zn : n = 0,1,2, be a branching process with offspring distribution X ~ Bin(2,...
2. Let(Zn : n = 0,1,2, be a branching process with offspring distribution X ~ Bin(2, ). That is, A r X=x | 0 | 1 | 2 | Total P(X = r) | 16 | 16 | 16 Find the probabhility that the process will eventually extinct
9. Consider the Branching Process {Xn,n = 0,1,2,3,...} where Xn is the population size at the nth generation. Assume P(...
9. Consider the Branching Process {Xn,n = 0,1,2,3,...} where Xn is the population size at the nth generation. Assume P(Xo = 1) = 1 and that the probability generating function of the offspring distribution is common A(z) (z3322z + 4) 10 (а) If gn 3 P(X, — 0) for n %3D 0, 1,..., write down an equation relating ^n+1 and qn. 0,1,2 Hence otherwise, evaluate qn for n= or (b) Find the extinction probability q = lim00 n 6 marks]...
extinct al U1 Exercise 9.12 Let μ a of Theorem et μ and σ 2 be...
extinct al U1 Exercise 9.12 Let μ a of Theorem et μ and σ 2 be the mean and vari 98 to show that the variance of Zn, ance of the family-size distribution. Adapt the proof the size of the nth generation of the branching process, is given by 2 nơ if, 1, Theorem 9.8 The mean value of Zn is (9.9) where u - kp is the mean of the family-size distribution Proof By the theory of probability generating...
(1) Consider the following processes: There are No = 1 many individuals in the zeroth generation. The number of individuals N in the kth generation comes from each individual in the (k-1)th generatio...
(1) Consider the following processes: There are No = 1 many individuals in the zeroth generation. The number of individuals N in the kth generation comes from each individual in the (k-1)th generation having Poisson(A) many offspring independent of all others. (a) Find a formula for E(Nk). (b) Suppose X1. Show that P(Nk 0) converges to unity as ko N. = 0) converg (2) Consider the processes from the previous problem modified so that the number of offspring which each...
Exercise 5 (Sample variance is unbiased). Let X1, ... , Xn be i.i.d. samples from some...
Exercise 5 (Sample variance is unbiased). Let X1, ... , Xn be i.i.d. samples from some distribution with mean u and finite variance. Define the sample variance S2 = (n-1)-1 _, (Xi - X)2. We will show that S2 is an unbiased estimator of the population variance Var(X1). (i) Show that ) = 0. (ii) Show that [ŠX – 1908–) -0. ElCX –po*=E-* (Šx--) == "Varex). x:== X-X+08 – ) Lx - X +2Zx - XXX - 1) + X...
1. Let X be an iid sample of size n from a continuous distribution with mean...
1. Let X be an iid sample of size n from a continuous distribution with mean /i, variance a2 and such that Xi e [0, 1] for all i e {1,...,n}. Let X = average. For a E (0,1), we wish to obtain a number q > 0 such that: (1/n) Xi be the sample Р(X € |и — 9. и + q) predict with probability approximately In other words, we wish to sample of size n, the average X...
show me all work for the problem i,ii,iii Exercise 1 (Sample size for estimating the mean)....
show me all work for the problem i,ii,iii
Exercise 1 (Sample size for estimating the mean). Let X1,...,x, be i.i.d. samples from some un- known distribution of mean u. Let X and S denote the sample mean and sample variance. Fix a E (0,1) and € >0. (i) Suppose the population distribution is N(uo?) for known op > 0. Recall that we have the following 100(1 - a)% confidence interval for : (1) Deduce that plue (x-Zalze in 2+ zarze...
Question 3 [25] , Yn denote a random sample of size n from a Let Y,...
Question 3 [25] , Yn denote a random sample of size n from a Let Y, Y2, population with an exponential distribution whose density is given by y > 0 if o, otherwise -E70 cumulative distribution function f(y) L ..,Y} denotes the smallest order statistics, show that Y1) = min{Y1, =nYa) 3.1 show that = nY1) is an unbiased estimator for 0. /12/ /13/ 3.2 find the mean square error for MSE(e). 2 f-llays Iat-k)-at 1-P Question 4[25] 4.1 Distinguish...
I figured the number 380.25 should related to quadratic model. is it correct> if it is,...
I figured the number 380.25 should related to quadratic model.
is it correct> if it is, how did he get this number tho. if not,
how did he get the number
Thanks
Problem For Exercise 12.8 on page 451, construct a 90%_cenidence inteaval for the mean compressive strength when the concentration is x = 19.5 and a adratic model used 12.8 The following is a set of coded experimental cata on the compressive strength of a particular alloy at var-...
Problem 2. Problem 1 doesn't need to be done, it's here for
reference
166 Branching processes is a branching process whose .... is a branchin the result zes have mean μ (s l ) and variance σ 2, then var( ZnJun of Problem 9.6.1 to show that, if Zo. z 2. Use ditioning on the value of Zm, show th ose fa outition theorem and conditioning on the value of Z 9.6 Problems I. Let X1 , X2. . ....
2. Let(Zn : n = 0,1,2, be a branching process with offspring distribution X ~ Bin(2, ). That is, A r X=x | 0 | 1 | 2 | Total P(X = r) | 16 | 16 | 16 Find the probabhility that the process will eventually extinct
9. Consider the Branching Process {Xn,n = 0,1,2,3,...} where Xn is the population size at the nth generation. Assume P(Xo = 1) = 1 and that the probability generating function of the offspring distribution is common A(z) (z3322z + 4) 10 (а) If gn 3 P(X, — 0) for n %3D 0, 1,..., write down an equation relating ^n+1 and qn. 0,1,2 Hence otherwise, evaluate qn for n= or (b) Find the extinction probability q = lim00 n 6 marks]...
extinct al U1 Exercise 9.12 Let μ a of Theorem et μ and σ 2 be the mean and vari 98 to show that the variance of Zn, ance of the family-size distribution. Adapt the proof the size of the nth generation of the branching process, is given by 2 nơ if, 1, Theorem 9.8 The mean value of Zn is (9.9) where u - kp is the mean of the family-size distribution Proof By the theory of probability generating...
(1) Consider the following processes: There are No = 1 many individuals in the zeroth generation. The number of individuals N in the kth generation comes from each individual in the (k-1)th generation having Poisson(A) many offspring independent of all others. (a) Find a formula for E(Nk). (b) Suppose X1. Show that P(Nk 0) converges to unity as ko N. = 0) converg (2) Consider the processes from the previous problem modified so that the number of offspring which each...
Exercise 5 (Sample variance is unbiased). Let X1, ... , Xn be i.i.d. samples from some distribution with mean u and finite variance. Define the sample variance S2 = (n-1)-1 _, (Xi - X)2. We will show that S2 is an unbiased estimator of the population variance Var(X1). (i) Show that ) = 0. (ii) Show that [ŠX – 1908–) -0. ElCX –po*=E-* (Šx--) == "Varex). x:== X-X+08 – ) Lx - X +2Zx - XXX - 1) + X...
1. Let X be an iid sample of size n from a continuous distribution with mean /i, variance a2 and such that Xi e [0, 1] for all i e {1,...,n}. Let X = average. For a E (0,1), we wish to obtain a number q > 0 such that: (1/n) Xi be the sample Р(X € |и — 9. и + q) predict with probability approximately In other words, we wish to sample of size n, the average X...
show me all work for the problem i,ii,iii
Exercise 1 (Sample size for estimating the mean). Let X1,...,x, be i.i.d. samples from some un- known distribution of mean u. Let X and S denote the sample mean and sample variance. Fix a E (0,1) and € >0. (i) Suppose the population distribution is N(uo?) for known op > 0. Recall that we have the following 100(1 - a)% confidence interval for : (1) Deduce that plue (x-Zalze in 2+ zarze...
Question 3 [25] , Yn denote a random sample of size n from a Let Y, Y2, population with an exponential distribution whose density is given by y > 0 if o, otherwise -E70 cumulative distribution function f(y) L ..,Y} denotes the smallest order statistics, show that Y1) = min{Y1, =nYa) 3.1 show that = nY1) is an unbiased estimator for 0. /12/ /13/ 3.2 find the mean square error for MSE(e). 2 f-llays Iat-k)-at 1-P Question 4[25] 4.1 Distinguish...
I figured the number 380.25 should related to quadratic model.
is it correct> if it is, how did he get this number tho. if not,
how did he get the number
Thanks
Problem For Exercise 12.8 on page 451, construct a 90%_cenidence inteaval for the mean compressive strength when the concentration is x = 19.5 and a adratic model used 12.8 The following is a set of coded experimental cata on the compressive strength of a particular alloy at var-...
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