2. (20 points) Use first principles to find the autocorrelation function for the stationary process defined...
2. Consider the time series X, = 2 + 0.5t +0.8X1-1 + W, where W N(0.1). (a) (8 points) Calculate E(X2) Is this process weakly stationary? Give reasons for your answer. Hint: Find the mean function of {X) and then substitute t = 20. (b) (3 points) Calculate Var(X20) Question 2 continues on the next page... Page 4 of 12 c)(4 points) Consider the first differences of the time series above, that is Is {%) a weakly stationary process. Prove...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
answer all 4 questions 2+1) π i Given that :-., and arg( 4. Find Find 2. Use the first principles to find the derivative of [20] cos(x-4x) . rt k! 3. Use derivative to show that [10] 4. Find dry, if y = xx, 2+1) π i Given that :-., and arg( 4. Find Find 2. Use the first principles to find the derivative of [20] cos(x-4x) . rt k! 3. Use derivative to show that [10] 4. Find dry,...
Question 3 (20 Points For each spectral density function defined below, determine the mean-square value of the random process. Show your work for full credit. ω) = else (2π)2 +25 (2mf+37(2)2+36 (s+0.5)(s-0.5) ω2 +25 w" +37a, 2 +36 TO (a)- Question 3 (20 Points For each spectral density function defined below, determine the mean-square value of the random process. Show your work for full credit. ω) = else (2π)2 +25 (2mf+37(2)2+36 (s+0.5)(s-0.5) ω2 +25 w" +37a, 2 +36 TO (a)-
QUESTION 6 (20 Marks) CO CO6 Marks20 Use five decimals points throughout your calculations when solving this question. Evaluate the performance of fourth order Runge-Kutta (RK-4) by using different values of h using the given function. The analytical value of y-r+21+1-0.5e Rungo-Kutta 4 Oder Equation Page 12/21 Firal Esam, SKKK 2133 1617-1 You are given an option to select h癰 0.5. a 45, 0.4, 0.35, 0.3 and h 0.25), to solve the (a) given function. Which h can give the...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
Identify the argument of the function. 1 2./ 3 .031 Use the unit circle to find all values of between 0 and 2 for the following Enter your answers as a comma-separated list.) tan . 3.-/2 points Trigo 3.3.043 Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find the sine and cosine of the angle to the nearest ten thousandth 2100 sin 210°C COS 2100...
i need help with 3-9 pret uie ale he appluly dlagonal line of data points. For reference, the values for the Sun are M +4.85, B-V +0.63. 2. Theoretical Stellar Models and Evolutionary Tracks The theoretical Zero-Age Main Sequence' (-ZAMS) is defined as the set of computer models representing stars that have just started converting H to He in their cores via thermonuclear fusion. a. Plot the 4 ZAMS data points for each mass from Table 3. Then connect those...
Question 1 An array is NOT: A - Made up of different data types. B - Subscripted by integers. C - A consecutive group of memory chunks. D - None of the choices. Question 2 How many times is the body of the loop executed? int i=1; while(true) { cout << i; if(++i==5) break; } A - Forever B - 4 C - 5 D - 6 E - 0 Question 3 What is wrong with the following piece of...