(a∗ ) Compute P(X = 4, Y = 5). (b∗ ) Compute the marginal pmf’s of X and Y . (c∗ ) Are X and Y independent?  Let Z be the minimum of X and Y . Calculate E[Z].

Q: 18-21. The production function for making widgets is P(x, y) = 4,600x³/Bys/8 Where p is the number…

A: The production function is given by, Px,y=4600x3/8y5/8

Q: The figure below shows the level curves of a function f(x, y) around a maximum or minimum, M. The x-…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: Jerry has a total of I dollars per year to spend on apples (x) and Polo-shirts (y). His preferences…

A: Given that, Jerry has a total of I dollars per year to spend on apples (x) and polo shirts (y).…

Q: f(x,y)=x² +16xy + y² +8

A:

Q: Find fzyr. f(x, y, z) = x³y5₂6 + xy³ + yºz

A: Given: fx,y,z=x3y5z6+xy3+y6z We have to find fzyx For fzyx we first have to find the partial…

Q: a) estimate fx (1,0) and fy (1,0), explain b) estimate fx (0,0) and fy (0,0), explain

A: The contour map of a function is given as follows, where the level curves are labelled by the…

Q: Let r(t) =ti +t³j +tk The normal component of acceleration is an = 6t/2/V9t4 + 2 а. b. an= 4t/2/V9r*…

A:

Q: a) Consider the utility function of Carin where: (i) 1/2 U (9₁, 92) = 3 × 9₁ 1/3 x 92 91 = total…

A: Here we have to find marginal utilities of product 1 and 2

Q: Do one gradient descent step for finding the minimum of S(r, y) = 3r- ry + 2y + 2r +3y %3D starting…

A: Given function is  fx,y=3x2-xy+2y2+2x+3y             (i) To perform one gradient descent step for…

Q: . Find div(F x G) = V · (F × G). F(x, y, z) = i + 9xj + 3yk G(x, y, z) = xi - yj + zk div(F x G) =

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 2. Suppose that X and Y have the following joint PMF: P» (x,y) Y X 1 2 0.10 4 0.15 6 0.10 0 0.15…

A: The joint PMF of X and Y is  PX,Y(x,y)              Y X 0 1 2 2 0.15 0.10 0.10 4 0.20 0.15…

Q: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

A:

Q: Find the gradient function for: 1+3x 1) y = %3D x2 +1

A: Given that  y=(1+3x)/(x^2+1) To find the gradient of y

Q: Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin (t). Find af af and (write your…

A:

Q: Determine whether the function f(x, y) = y extrema on R2 (i.e. it is defined for all a's and y's).…

A:

Q: 2. Calculate the gradient of the function shown and evaluate it at the point (-1,1) f(x,y) = xy²-yx²

A: Approach to solving the question: Concept:The gradient of a function gives us a vector that points…

Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

A: Introduction: A function's maximum directional derivatives at a particular point P are produced in…

Q: The equation f(x, y, z) = exyz+z=1 + e implicitly defines z as a function z = g(x,y) of x and y.…

A:

Q: 10. Let y = e4=*y¬3y°. Let F be the gradient of 9. Let C be a circle of radius 4, centered at (3,…

A: Given: Let F be the gradient of φ. ⇒∇φ=F Now, Circulation =∬S ∇×F. n^ ds      =∬∇×∇φ.n^ ds

Q: 2. Using difference quotients, estimate f,(3, 2) and S,(3, 2) for the function given by S(x, y) =…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.