Given: x-torch.TensorCEC1, 2, 3], [1, 2, 3]]).viewC-1, 2) y- torch.TensorCCE2, 1]]).view(2, -1) How would you calculate...
dr - 0 dz 1 dx P x² + y² + 하공 8. OP 11 위공 d츠 1 ㅇ d² 0= 이 1) Here are two rank 1 tensors of differing types, written in Cartesian co-ordinates: 1 -4 vi(x, y, z) = wi(x,y,z) 2 3 a) Calculate their scalar product viw. (2 marks) b) Using the appropriate tensor transform equations, and expressions for the partial derivatives obtained from class, transform both tensors into cylindrical polar co-ordinates (r, 0, z). (6...
Consider a consumer whose utility function is given by U(x, y) = x^1/3 y^2/3, where x and y represent quantities of consumption of two consumer goods. (a) If the consumer’s income is $100 and the prices of x and y are both $1, how should the consumer maximize her utility? What is her maximum level of utility? (b) If the price of y rose to $2, what would be the resulting income and substitution effects? Illustrate your answer.
Assume that you are given an image showing the intensity I(x, y) = c exp[-a(x-b)2]. How does the image look like? Can you compute the corresponding Hessian matrix at pixel (x,y)? Does it tell us anything about the image
13. Let X and Y be rv's whose joint PMF is given by: Y=1 2 3 X=0 0.2 0.1 0 1 0.1 0.3 0. 2 . 0 0 0.3 Compute the covariance and correlation matrix of the random vector (X,Y).
Parts d and e needed!
1) Here are two rank 1 tensors of differing types, written in Cartesian co-ordinates: 1 -4 vi(x, y, z) = wi(x,y,z) 2 3 a) Calculate their scalar product viw. (2 marks) b) Using the appropriate tensor transform equations, and expressions for the partial derivatives obtained from class, transform both tensors into cylindrical polar co-ordinates (r, 0, z). (6 marks) c) Calculate the scalar product of the transformed tensors, and show that the answer is the...
Matrices multiplication and Partitioned multiplication: matrix X= 2 1 5 4 2 3 Matrix Y= 1 2 4 2 3 1 1. Find the XY^(T) T means transpose 2.Compute the outer product expansion of XY^(T) . 3. did you get the same answer from 1 and 2?
1-Calculate the pdf of y given that the pdf of x is given by pdf
x
2- cketch of pdf
iVen a random variable y- 5x of where x is another random variable. Calculate the p y given that the pdf of x is given by and drow pdf -X x20
3 1 Calculate ou. Given U(x,y) -4y4x4
Calculate the following for the random vector (XY) with joint pdf fixy)--(3/4)(x+y) if 2x<yco, -1<x<o. 1. The marginal pdf of X and the marginal pdf of Y. Are X and Y independent random variables? 2. The expected value and variance of X and Y respectively. 3. The joint cdf in the case 2x<y<0. -1<x<0. 4. The expected value of the random variable Z defined as X^2 times Y^2. 5. The covariance between X and Y. 6. The expected value and...
3. (25 pts) Consider the data points: t y 0 1.20 1 1.16 2 2.34 3 6.08 ake a least squares fitting of these data using the model yü)- Be + Be-. Suppose we want to m (a) Explain how you would compute the parameters β | 1 . Namely, if β is the least squares solution of the system Χβ y, what are the matrix X and the right-hand side vector y? what quantity does such β minimize? (b)...