Q1] Test for linearity, time invariance, causality, BIBO stability, and static of the systems ii) y(n)=()"x(n)
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- New Question: Is it possible to clarify the following Bartleby Expert Answer, with any Signs (/, *, +,-) and/or Positions (^, XY, Xy) that may be helpful? Thank you! (Original Question is also provided). Original Question: 2. A small oil company considers the continuous pumping of oil from a well as a continuous income stream, f(t) = 600e-0.2: in thousands of dollars per year. (a) (10) Find an estimate of the total income from this well over the next 10 years.b) Let aggregate national income be given by Y; = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Ct = mY; Investment is given by Iį = i + a(Yt-1 – Yt-2) And government expenditure declines over time according to G; = Go(1 – 8)*, 0 < 8 < 1 Where d is the exogenous rate of decline of government expenditure (i) Derive the linear second order difference equation. (ii) Solve the difference equation.12) f(x, y) =x' +y'+3x-3y -8 Ans. f(0,0) saddle point, S(0,2)=-21 local min., f(-2,0)=-4 local max., f(-2,2) saddle point
- 2 Linearization Linearize the following: a) y(t) = t² + 2t - 2 in the range 1For the points given (1, 5), (2, 7), (3, 6), (4, 10) use partial derivatives to obtain the formula for the best least-squares fit to the data points.O Consider a polynomial regression model Y; = Bo + 31X; + B2X? + ...+ B,X; + u;, where E (u;|X;, X?,..., X;) = 0, observations (Y;, X;) are independent and identically distributed and 0 < E (Y;*) < o, 0 < E (X") < o. How is the OLS estimation affected if we estimate a linear regression (r = 1) when the true form of the regression function is quadratic (r = 2) or cubic (r = 3)? %3DFind y= y -complementary + y-particularThe Linear approximation (linearization) of f (x) = at x = 2 is %3D %3D (A) y = } - (* –) %3D (B) y = } - (x – 2) (C) y = } - (x – 2) (D) y = - (x – 2) (E) y %3D 3-유(z- 2) %3D 3. %3D 16 Y = 8.Linear regression was performed on a dataset and it was found that the best least square fit was obtained by the line y = 2x + 3. The dataset on which regression was performed was corrupted in storage and it is known that the points are (x, y): (-2,a), (0,1), (2, B). Can we recover unique values of a, B so that the line y = 2x + 3 continues to be the best least square fit? Give a mathematical justification for your answer.8) The relationship between the TSLS slope and the corresponding population parameter is: (Z; - Zju; i=1 A) (§ 7SLS - B1) = E (Zi - ZX; - X) i=1 £ (Z; - Z) i=1 B) (§ ȚSLS - B1) = £ (Zi - Z(X¡ - X) i=1 1 TSLS i=1 E (Zi - Z2 i=1 (X; - Xju; i=1 D) (§ SLS - B1) = - E (Z; - ZxX¡ - X) i=1 9) In the Fixed Effects regression model, using (n – 1) binary variables for the entities, the coefficient of the binary variable indicates: A) the level of the fixed effect of the ith entity. B) will be either 0 or 1. C) the difference in fixed effects between the ith and the first entity. D) the response in the dependent variable to a percentage change in the binary variable. 10) In the Fixed Time Effects regression model, you should exclude one of the binary variables for the time periods when an intercept is present in the equation: A) because the first time period must always excluded from your data set. B) because there are already too many coefficients to estimate. C) to avoid perfect…Q1: (): Let Y, ., Y, be order statistics of a random sample of size 4 from Exponential (10). Find g(yı), g(y1, Y3)and P(Y, > 100). V4-x2 Q2: (): Let f(x) = ,0 sx< 2, zero elsewhere. Let Y = 1 - Find g(y) by transformation method.Use partial derivatives to obtain the formula for the best least-squares fit to the data points. (1,5), (2,5), (3,11) y = (Simplify your answer. Use integers or decimals for any numbers in the expression.)SEE MORE QUESTIONS