Conditioned branching process. Consider a branching process whose family sizes have thegeometric mass function f(k): apk, k≥ 0, where μ = p/q > 1. Let Zn be the size of the nthgeneration, and assume Zo = 1. Show that the conditional distribution of Zn/u", given that Zn > - 0,converges as n → ∞ to the exponential distribution with parameter 1 - µ-¹.=

Answered: Image /qna-images/answer/7c8082cb-8e3c-412a-9edc-6916ec655561.jpg

Answered: Conditioned branching process. Consider…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose a high-tech shop opens at 9 am. During the release of a long-waited new generation smart phone people start arriving at the shop at 8 am and queue in front of the shop. The arrivals follow a non-homogeneous Poisson process with rate function λ(t) = 25t2 (t = 0 refers to 8 am and t = 1 to 9 am). (a) Find the distribution of the number of people waiting in front of the shop when the shop opens. (b) If we know that exactly 30 people are waiting in front of the shop at 9 am, what is the probability that exactly 20 of them arrived between 8.30am and 9 am? (c) Calculate the average waiting time of a person who is present at 9 am.
Suppose Xn is the sample mean of a random sample of size n from a distribution that has a Gamma(2,1/2) (where a = 2, B = }) pdf f(x) = 4xe-2a, 0 < x < ∞, zero elsewhere. Use the Central Limit Theorem to deduce that the random variables Vn(Xn – 1) converges in distribution to N(0, 1/2).
Assume that a time-series plot takes the form of that shown in the following graph: 80 60 60 40 40 20 20 * -20 ** * -40 0 2 4 6 8 10 12 Given this plot, which of the following models would likely give the best fit? O ^ = bo + bit + by + bị t lý = bo + bit + bit ŷ = bob₁ + b₁t On =bo+ bạt + biết biết ba
A time series {yt} follows an MA(2) model: Yt = 2 + Ut +0.54t-1 + 0.4ut-2. Assume that ut is a white noise series with a mean of O and a variance of 2. Please calculate Var(yt) (i.e. the variance of) 2.96 1.41 2.82 O 1.98
Determine the single equivalent rate of discount for the discount series 20%, 13%, and 4%. (1-d₁) = (1-d₂) = de 1-[(1 - ₁) (1 - d₂) (1 - d3)] = Single Equivalent Rate of Discount = places) (1-d3) = (rounded to four decimal places) % (rounded to two decimal
Statistics and Probability 1. What is a (nonhomogeneous) Poisson process with rate A(t) = t² (write down it defini- tion) ? What real life phenomenon may a Poisson process model?
1
Find the maximum likelihood estimator of the unknown parameter where X₁, X2,..., X₂ is a sample 0 from the distribution whose density function is fx(x) = { e-(1-0) if x > 0 otherwise.
5.2. Consider the sequence defined by xo = a > 0 and a Xk + Xk Xk+1 = Prove that this sequence converges to X* = Vā and that the convergence rate is quadratic, and determine the rate constant.
insurance math no. 9
-x2 (18) a) Using the Maclaurin series for f(x) = e* find a power series representation for g(x) = e -x? b) The generalized normal distribution function d(z) = 1 e 2 dx calculates the probability 27 that a standard normal variant assumes a value in the interval [0,z]. Use at least four terms from your series in a) to approximate the probability that a standard normal variant will fall in the interval [0,1].
b) Sketch the probability mass function and the cumulative distribution function of X (c) Consider a random sample of 6 parcels. If Y is the number of parcels taking longer than 1 day to arrive, write down the distribution of Y and its mean and variance.

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