Two teams A and B play a soccer match. The number of goals scored by Team A is modeled by aPoisson process N₁ (t) with rate X₁ = 0.02 goals per minute, and the number of goals scored byTeam B is modeled by a Poisson process N₂ (t) with rate A₂ = 0.03 goals per minute. The twoprocesses are assumed to be independent. Let N(t) be the total number of goals in the game upto and including time t. The game lasts for 90 minutes.a. Find the probability that no goals are scored, i.e., the game ends with a 0-0 draw.b. Find the probability that at least two goals are scored in the game.c. Find the probability of the final score beingTeam A: 1, Team B: 2d. Find the probability that they draw.

It is given that two teams A and B play a soccer match.The number of goals scored by team A is…

Answered: Two teams A and B play a soccer match.…

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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Prove the following property of the compound Poisson process:1. E(xt) = λ t E(Y).
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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.
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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