ID1=2 IN=19 Q.1. Fit a straight line to the x and y values y = a + ax х IN+2 2*ID1 IN+4 IN+5 IN+8 IN+15 3*ID1+1 3*ID1+2 4*11 5*ID1+6 y Fill the following Table by using excel and find the following values х х*у y St frit x2 Sr ао ai r2
You have two fair 6-sided dice. One is red and the other is blue. When you roll them X=red-blue and Y=red+blue. a) Find the joint distribution of (X,Y). b) Find the covariance of X and Y
6. Consider the following constrained maximization problem: 2 5 tu (х, у) x7y7 max х,у s.t Рxх + pуy < м 3, py = 4, M = 12. Answer the following questions with px a. Write down the Lagrangian function b. Derive the first order conditions c. Derive the optimality condition from those conditions d. Write the other optimality condition (since there should be two in order for us to solve for two unknowns) e. Find the optimal values for...
Consider the following. у y=x (1,1) х 2 4 6 10 -2 x = 8 -4 y = 2 - x -6 -8 (a) Form the integral that represents the area of the shaded region. dx (b) Find the area of the region. (Give an exact answer. Do not round.)
Given f(x,y) = 2y + 3y + yin(x) + x, find af ах +5 X af — 12ух -7+езу, у +1 ах af = 2ух -6+ у ах Х Од у 1 = 2ух -6+ ах Х о af 12ух-74У +1 ах Х
Consider joint probability distribution given below y fxy (x, у) х 1.0 1 11/32 1/32 1.5 2 1.5 1/4 2.5 4 1/4 3.0 1/8 Determine the following: In your intermediate calculations, round all fractions to three decimal places. Round your answers to three decimal places (e.g 98.765) (a) Conditional probability distribution of Y qiven that X = 1,5. у Fуus 0) 1 2 3 5 (b) Conditional probability distribution of X given that Y 2. 1.0 1.5 2.5 (c) E(YIX...
Question 10 [8 points] Find all values of x so that the triangle with vertices A=(-3, X, 3), B=(-2,0, 6), and C=(-4,-2, 7) has area 5. x=???
5. Let f R2 ->R2 be the function given by f(x, y) (х + у, х — у). (i) Prove that f is linear as a function from R2 to R2. (ii) Calculatee the matrix of f. (iii) Prove that f is a one-to-one function whose range is R2. Deduce that f has an inverse function and calculate it. (iv) If C is the square in R2 given by C = [0,1] x [0, 1], find the set f(C), illustrating...
[ İID Finding Intercepts Algebraically In Exercises 45-54, find the x- and y-intercepts ERİ of the graph of the equation algebraically. 45. У-12-5x 47, y =-3(2x + 1) 46. y 16-3 48, y = 5-(6-x) 51. 4y-0.75x + 1.2 = 0 52, 3y + 2.5x-3.4 = 0 8x 54. + 50-2y = 0
We will rank the y-values of the following data set: х 5 6.5 8.6 9.2 10.7 12.8 14 15.5 у - 12.9 - 10.2 -12.9 -26.3 -38.7 -38.7 49.6 -41.5 The scatterplot of the data looks like this: . Assessments ine scatterpot or the data VOKS URE : M17 Problem Set . . . Fill in the following table: Fill in the following table: X y X-rank y-rank 5 -12.9 1 6.5 - 10.2 2 8.6 -12.9 3 9.2 -26.3...