Homework Answers
Considering the values of a,b in (0,1) there is possibility of an arrays of value of a such that
aα+(1-a)α''≻α'
Similarly there is other set of values of b fro (0,1) such that
α'≻bα+(1-b)α"
It just represents the syntax of Convex hull where U(aα+(1-a)α'')>U(α') and on the other hand we have U(α')>U(bα+(1-b)α'')
This axiom is generally used in expected utility settings
For an instance assume
α= Visiting Paris through Air travels ; α''=Death while travelling due to terrorist attack over a same plane
α'= Watching Paris on Video at home
This means if we place as low possible probability on Death we will always prefer to go to Paris that is
aα+(1-a)α''≻α' but as soon as we weigh incident of death heavily we start to opt α'≻bα+(1-b)α"
This is the layman meaning of this axiom
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I only need Question 4 (Image above) answered. I am providing you with the rest of the questions and other information...
I only need Question 4 (Image above) answered. I am
providing you with the rest of the questions and other information
for background information since it is necessary to answer Question
4. I do not need answers to Q1, 2 and 3 - only for Q4
Background information for the question:
The dataset weightloss.dta contains information on 77 patients
randomised to undertake one of three diets (referred to as diet A,
B and C). Some background information is also available,...
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Consider the following AR(1) model: 1. a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. the following random 2. Consider walk model: yeBo yt-1 +ut, t-0,1,..,T a. Show that yt-3βο + yt-3 + ut + ut-1 + ut-2. b. Suppose that 0-0, show that y.-t βο +4 + ut-1 + + u! c. Suppose that that yo -0, and ut for all t are ii.d. with mean 0 and variance...
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1. Consider the following AR(1) model: a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. b. Show that 1 t-2 2. Consider the following random walk model: ytBo yt-1 +ut, t 0,1,...,T Show that ye 3o yt-3 + ut + Ut-1 +t-2 Suppose that yo - 0, show that yt - tPo + ut + ut-1++u, Suppose that that yo -0, and ut for all t...
4.4.16. Consider two matrices Ayxn and Bmxk. (a) Explain why rank (A | B) = rank (A) +rank (B) - dim (R(A) R(B)). Hint: Recall Exercise 4.2.9. (b) Now explain why dim N ( A B) = dim N (A)+dim N (B)+dim (RA) R (B)). (c) Determine dim (R(C) ON (C)) and dim (R(C) + N (C)) for -1 1 1 -2 1 -1 0 3 -4 2 C= -1 0 3 -5 3 -1 0 3 -6 4 1-1...
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1. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01 (1) 60 = {1, 1421 a) Find the state transition matrix and the impulse response matrix of the system. b) Determine whether the system is (i) completely state controllable, (ii) differentially control- lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. c) Repeat part (b) for to = 1. d) Determine whether the system is (i) observable, (ii) differentially observable, (iii) instanta-...
3) Consider the following linear regression: y =a + Bx + Show that minimizing the sum of squared residuals ( - ) to obtain OLS estimators of the slope and the intercept results in the following algebraic properties a) b) Ex = 0 = 0 4) You run the following regression: TestScore = a + (Female) + where TestScore is measured on a scale from 400 to 1000, and female is an indicator for the gender of the student. You...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
I only need Question 4 (Image above) answered. I am
providing you with the rest of the questions and other information
for background information since it is necessary to answer Question
4. I do not need answers to Q1, 2 and 3 - only for Q4
Background information for the question:
The dataset weightloss.dta contains information on 77 patients
randomised to undertake one of three diets (referred to as diet A,
B and C). Some background information is also available,...
Help with Pascal’s Triangle: Paths and Binary
Strings
Suppose you want to create a path between each number on Pascal's Triangle. For this exercise, suppose the only moves allowed are to go down one row either to the left or to the right. We will code the path by using bit strings. In particular, a O will be used for each move downward to the left, and a 1 for each move downward to the right. So, for example, consider...
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