Could you solve (ii), (iii), (iv)?Thank you. Q5 Let {N(t), t > 0} be a Poisson process with rate = 2. ComputeQ5 (i.) P(N(5) = 4, N(6) = 9, N(10) = 15).Q5 (ii.) P(N(5) – N(2) = 3).Q5 (ii.) P(N(5) – N(2) = 3, N(7) – N(6) = 4).Q5 ίv.) P(N(2) + N(5) = 4).Q5(v.) E[N(5) – 2N(6)+3N(10)].Q5 (vi.) Var[N(5) – 2N(6) +3N(10)].Q5 (vii.) Cov[N(5) – 2N(6),3N(10)].|

The given is Poisson process with rate λ=2.

Answered: Q5 Let {N(t), t > 0} be a Poisson…

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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Let {N_1(t)} and {N_2(t)} be two independent Poisson processes with rates λ1=1 and λ2=2, respectively. Find the probability that the second arrival in N_1(t) occurs before the third arrival in N_2(t). Round answer to 4 decimals.
Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)
1 Suppose that X is a stochastic process with dynamics dXt = µdt +σdWt , where W is a P-Brownian motion. The drift µ and the volatility σ are both constants. Find if there is a measure Q such that the drift of process X under Q is η(∈ R) instead of µ.
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This is a Stochastic Process question. Each customer makes claims following a Poisson process with rate 0.44 per year.For Scheme A, there are 3 discount levels: 0%, 10% and 20%.For a customer in Scheme A, he or she will move between discount levels throughout the year at continuous times.The annual premium to be paid at the start of each year is determined by the discount level he or she is in at that point of time, irrespective of the movements between the discount levels throughout the year.If a customer in Scheme A makes a claim, he or she will immediately move to a worse discount level, if possible, or remain in the 0% level.Independently of the customer making claims, for each customer in Scheme A independently the insurance company will perform a 'bump' where the customer will move to a better discount level if possible (or remain iin 20% otherwise) every so often as a customer loyalty programme with time between bumps exponentially distributed with mean 2 years. Find the…
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Find the equilibrium solution for P. Furthermore determine whether P is initially increasing faster if the initial population is 120 or 200.
Time series decomposition seeks to separate the time series (Y) into 4 components: trend (T), cycle (C), seasonal (S), and irregular (I). What is the difference between these components? The model can be additive or multiplicative.When we do use an additive model? When do we use a multiplicative model?
a man is investigating the populaion of bear in two areas. Area 1 and Area 2. He expect the number of bear to be X and Y in area 1 and area 2 to be Poisson- distributeted. He expect the number og bear to be λ1 = 3 in area 1 and λ2 = 5 in area 2. Find P(X = 2) and P(X ≥3) and find an approximate value expression for P(X = Y)
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The manager of a market can hire either Mary or Alice. Mary, who gives you service at an exponential rate 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model. Assume customers arrive at a Poisson rate of 10 per hour. a) What is the average cost per hour if Mary is hired? If Alice is hired? b) Find C if the average cost per hour is the same for Mary and Alice.

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