If {N₁ (t)} and {N₂(t)} are two independent Poisson processes withratesy and μ respectively then N₁ (t) – N₂(t) isSelect one:a.a Poisson process with rate y - flO b.not a Poisson processa Poisson process with rate y + μl.O d. a Poisson process with rate fl

If {N(t)} and {N2(t)} are two independent Poisson processes with rates y and μ respectively then…

Answered: If {N₁(t)} and {N₂(t)} are two…

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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Using statistical power analysis
K1
Q5 Let {N(t),t > 0} be a Poisson process with rate A = 2. Compute Q5 (i.) P(N(5) = 4, N(6) = 9, N(10) = 15). Q5 (ii.) P(N(5) – N(2) = 3). - Q5(iii.) P(N(5) – N(2) = 3, N(7) – N(6) = 4). %3D Q5 (ίv.) P (N(2) + N(5) -4). 05 ν.) E[Ν(5) -2N() +3N (10)]. Q5(vi.) Var[N(5) – 2N(6)+3N(10)]. Q5(vii.) Cov[N(5) – 2N(6), 3N(10)].
b) Let X(t) be a zero mean, stationary, Gaussian process with autocorrelation function R (T). This process is applied to a square law device defined by the input-output relation Y(t) = X(t), where Y(t) is the output. i) Show that the mean of Y(1) is R (0). ii) Find out the autocovariance function of y(t).
x(t) == ()-1 h(t)=pt .u(t) y(t) Z(t) is a sequence of Poisson impulses. X is the expected number of impulses per Find a unit time E[Ÿ(t)] b) Ryy (T).. c) Syy (w)
How do you get the red one from the last step?If there is something wrong with the steps?I am not sure,if we can,could you show me how does it work?Thank you!
5 The relation between the input X (t) and Y (t) of a system is Y (t) = X² (t). X (t) is a zero mean stationary Gaussian random process with auto correlation function (T) = e- RxX = e- a ld for a > 0. Find E[Y (t)] and Ryy (t).
Answer the next two questions based on the information given in the following Exhibit: Exhibit: The stock price S of an underlying security follows the geometric Brownian motion process ds = μS dt+oS dz, where z is a standard Wiener process. Then, 4. the process followed by S4 is a. dS4 = (4μ+0²)S4dt +40S³ dz ds4 = (4μ+602)S4 dt + 40S4 dz c. ds4 = us dt + os dz b. d. ds4 = (+40)S^dt +oSdz 5. the process followed by G(S, 1) = e(T-t)/S² is a. dG = (30²-2μ - r)Gdt - 20Gdz b. dG = (2μ-r)dt - 20Gdz c. dG = (30²-2μ r)Gdt + Gdz 1 16
Two teams A and B play a soccer match. The number of goals scored by Team A is modeled by a Poisson process N₁ (t) with rate X₁ = 0.02 goals per minute, and the number of goals scored by Team B is modeled by a Poisson process N₂ (t) with rate A₂ = 0.03 goals per minute. The two processes are assumed to be independent. Let N(t) be the total number of goals in the game up to 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 being Team A: 1, Team B: 2 d. Find the probability that they draw.
A random process is given by W(t)= AX(t) + BY(1), where A and B are real constants and X(7) and Y(1) are jointly WSS process. Find the a) power spectrum S(0) of W(t). b) Find S(W) if X(t) and Y(t) are uncorrelated.
A Random process X(t) is applied to a network with impulse response h(t) = u(t) exp (-bt) where b > 0 is a constant. The cross- correlation of X(t) with the output Y(t) is known to have the same form, Ryy(t) = u(t)t exp(-bt) (i) Find the auto-correlation of Y(t).
A random process is defined as Y (t) X (t) - X (- u), where X (t) is a WSS process and a > 0 is a constant. Find the PSD of Y (t) in terms of the corresponding quantities of X (t).

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If {N₁(t)} and {N₂(t)} are two independent Poisson processes with ratesy and µ respectively then N₁ (t) – N₂(t) is Select one: O a. a Poisson process O b. not a Poisson process O d. with rate y fl a Poisson process with rate y +μ. Ύ a Poisson process with rate fl