![[8] 6. Write the process SARIM A(0, 1, 1) (0,0,1)12 in an expanded form. Call the derived process Xt. Explain why Y7 VXt is s](http://img.homeworklib.com/questions/e5df5630-7964-11eb-a261-cbe0c2aa4d60.png?x-oss-process=image/resize,w_560)
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[8] 6. Write the process SARIM A(0, 1, 1) (0,0,1)12 in an expanded form. Call the...
1. Let {Xt} be a stationary process with mean μt = E(Xt) = 0 and autocovariance...
1. Let {Xt} be a stationary process with mean μt = E(Xt) = 0 and autocovariance function γX(k) = E(XtXt−k) - μ2 = E(XtXt+k) - μ2. De ne Yt = 5 + 2t + Xt. (a) Find E(Yt), the mean function for Yt. (b) Find γY (k), the autocovariance function for Yt in terms of γX (k). (c) Is Yt stationary? Explain. (d) De ne a new process Wt as Wt = Yt − Yt−1. Find E(Wt) and γW (k)....
2. Let (et) be a zero mean white noise process with variance 1. Suppose that the...
2. Let (et) be a zero mean white noise process with variance 1. Suppose that the observed process is h ft + Xt where β is an unknown constant, and Xt-et- Explain why {X.) is stationary. Find its mean function μχ and autocorrelation function p for lk0,1,.. a. b. Show that {Yt3 is not stationary. C. Explain why w. = ▽h = h-K-1 is stationary. d. Calculate Var(Yt) Vt and Var(W) Vt . (Recall: Var(X+c)-Var(X) when c is a constant.)...
Written in expanded form, the usual factorial function is n! = n middot (n - 1)...
Written in expanded form, the usual factorial function is n! = n middot (n - 1) middot (n - 2) ... 3 middot 2 middot 2 middot 1. The difference between elements in the product is always 1. It can be writ in recursive form as n! = n middot (n - 1)! (e.g., 10! = 10 middot 9!, 23! * 23 middot 22!, 4! = 4 3!, etc.). The purpose of this problem is to generalize the factorial function...
QUESTION 3 (a) Consider the ARMA (1, 1) process -Bat-1-where o and θ are model parame-...
QUESTION 3 (a) Consider the ARMA (1, 1) process -Bat-1-where o and θ are model parame- are independent and identically distributed random variables with mean 0 z, oz,-1 ters, and a1, a2, and variance σ (i) Show that the variance of the process is γ,- (ii) Using (i) or otherwise, show that the autocorrelation function (ACF) of the process is: ifk=0. (b) Let Y be an AR(2) process of the special form Y-2Y-2e (i) Find the range of values of...
2. The following table gives points on the Lorenz curve for the U.S. in 1970. 0 .6 8 .2 .4 L(x) 0 .323 .568 1 041 .149 a) Based on the table, the poorest 20% of the population in 1970 earned what per...
2. The following table gives points on the Lorenz curve for the U.S. in 1970. 0 .6 8 .2 .4 L(x) 0 .323 .568 1 041 .149 a) Based on the table, the poorest 20% of the population in 1970 earned what percent of the total income? b) The richest 20% of the population earned what percent of total income in the US, in 1970? Use a calculator or computer to find a quadratic curve best fit with form L(x)...
A Random Telegraph Signal with rate λ > 0 is a random process X(t) (where for each t, X(t) ∈ {±1}) defined on [0,∞) with the following properties: X(0) = ±1 with probability 0.5 each, and X(t) switches between the two values ±1 at the points of arrival of
A Random Telegraph Signal with rate λ > 0 is a random process X(t) (where for
each t, X(t) ∈ {±1}) defined on [0,∞) with the following properties: X(0) = ±1
with probability 0.5 each, and X(t) switches between the two values ±1 at the
points of arrival of a Poisson process with rate λ i.e., the probability of k changes
in a time interval of length T isP(k sign changes in an interval of length T) = e
−λT...
Consider an ideal gas of noninteracting bosons of mass m 0 in 3-D. 1. The fugacity z-eß-c"/hT of the gas can be expanded as a polynomial of the density ρ(-1/v yv): Find Ao, A, and A2. Useful form...
Consider an ideal gas of noninteracting bosons of mass m 0 in 3-D. 1. The fugacity z-eß-c"/hT of the gas can be expanded as a polynomial of the density ρ(-1/v yv): Find Ao, A, and A2. Useful formula: /2(e)+ .. 2. Ί1Kjaessme can bc expanded as The pre where po-is the pressure of a classicla ideal gas Without any calculation, determine the sign of B2, and explain your reason. Calculate B2 Sketch B2 as a function of temperature
Consider an...
-8 -24 -12 (16 points) Let A= 0 4 0 6 12 10 (a) (4 points)...
-8 -24 -12 (16 points) Let A= 0 4 0 6 12 10 (a) (4 points) Find the eigenvalues of A. (b) [6 points) For each eigenvalue of A, find a basis for the eigenspace of (b) [6 points) is the matrix A diagonalizable? If so, find matrices D and P such that is a diagonal matrix and A = PDP 1. If not, explain carefully why not.
Write a in the form a = a T+an N at the given value of t...
Write a in the form a = a T+an N at the given value of t without finding T and N. r(t) = (bet cos t) i + (6 et sin t)j + (6 et 13)k, t=0 a(0) = ( 1+ (ON (Type exact answers, using radicals as needed.)
2. Let (et) be a zero mean white noise process with variance 1. Suppose that the observed process is h ft + Xt where β is an unknown constant, and Xt-et- Explain why {X.) is stationary. Find its mean function μχ and autocorrelation function p for lk0,1,.. a. b. Show that {Yt3 is not stationary. C. Explain why w. = ▽h = h-K-1 is stationary. d. Calculate Var(Yt) Vt and Var(W) Vt . (Recall: Var(X+c)-Var(X) when c is a constant.)...
Written in expanded form, the usual factorial function is n! = n middot (n - 1) middot (n - 2) ... 3 middot 2 middot 2 middot 1. The difference between elements in the product is always 1. It can be writ in recursive form as n! = n middot (n - 1)! (e.g., 10! = 10 middot 9!, 23! * 23 middot 22!, 4! = 4 3!, etc.). The purpose of this problem is to generalize the factorial function...
QUESTION 3 (a) Consider the ARMA (1, 1) process -Bat-1-where o and θ are model parame- are independent and identically distributed random variables with mean 0 z, oz,-1 ters, and a1, a2, and variance σ (i) Show that the variance of the process is γ,- (ii) Using (i) or otherwise, show that the autocorrelation function (ACF) of the process is: ifk=0. (b) Let Y be an AR(2) process of the special form Y-2Y-2e (i) Find the range of values of...
2. The following table gives points on the Lorenz curve for the U.S. in 1970. 0 .6 8 .2 .4 L(x) 0 .323 .568 1 041 .149 a) Based on the table, the poorest 20% of the population in 1970 earned what percent of the total income? b) The richest 20% of the population earned what percent of total income in the US, in 1970? Use a calculator or computer to find a quadratic curve best fit with form L(x)...
Consider an ideal gas of noninteracting bosons of mass m 0 in 3-D. 1. The fugacity z-eß-c"/hT of the gas can be expanded as a polynomial of the density ρ(-1/v yv): Find Ao, A, and A2. Useful formula: /2(e)+ .. 2. Ί1Kjaessme can bc expanded as The pre where po-is the pressure of a classicla ideal gas Without any calculation, determine the sign of B2, and explain your reason. Calculate B2 Sketch B2 as a function of temperature
Consider an...
-8 -24 -12 (16 points) Let A= 0 4 0 6 12 10 (a) (4 points) Find the eigenvalues of A. (b) [6 points) For each eigenvalue of A, find a basis for the eigenspace of (b) [6 points) is the matrix A diagonalizable? If so, find matrices D and P such that is a diagonal matrix and A = PDP 1. If not, explain carefully why not.
Write a in the form a = a T+an N at the given value of t without finding T and N. r(t) = (bet cos t) i + (6 et sin t)j + (6 et 13)k, t=0 a(0) = ( 1+ (ON (Type exact answers, using radicals as needed.)
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