Problem 1. (12 Points) A point is uniformly distributed within the disk of radius 1. That...
Suppose that (X, Y) is uniformly distributed on the following right half disk. This half disk is the region inside the circle of radius 5 centered at the origin with positive x- coordinate. a) Give the joint probability density function of (x, y). b) Give the conditional probability density function of Y given X=x.
Suppose that (X, Y) is uniformly distributed on the following right half disk. This half disk is the region inside the circle of radius 5 centered at the origin with positive x- coordinate. a) Give the joint probability density function of (x, y). b) Give the conditional probability density function of Y given X=x.
Suppose that (X, Y) is uniformly distributed on the following right half disk. This half disk is the region inside the circle of radius 5 centered at the origin with positive x- coordinate. a) Give the joint probability density function of (x, y). b) Give the conditional probability density function of Y given X=x.
Suppose that (X, Y) is uniformly distributed on the following right half disk. This half disk is the region inside the circle of radius 5 centered at the origin with positive x- coordinate. a) Give the joint probability density function of (x, y). b) Give the conditional probability density function of Y given X=x.
Please explain and solve 3 Apl 2019 04) (25 points) The figure shows a non-conducting (thin) disk with a hole. The radius of the disk is Ri and the radius of the hole is R1. A total charge Q is uniformly distributed on its surface electric potential at infinity is zero, what is the el distance x from its center? (20 points) b) Use electric potential to determine the electric field at point P. (S points) . Assuming that the...
Problem 3 (25 points): Magnetic Field from Superposition. A circular disk of radius ro is uniformly coated with charge with a surface charge density of ps the disk lies in the x-y plane and the disk axis is the z-axis. This disk is spinning about the z-axis at a rate of one revolution every T seconds. The resulting surface current density on the disk is given by 2Tps a) What is the magnetic field intensity on the z-axis at a...
1. A total charge of Q is uniformly distributed around the perimeter of a circle with radius a in the x-y plane centered at origin as shown in Figure P4. (a) Find the electric field at all points on the z axis, i.e., (0,0,z). (b) Use the result you obtain in (a) to find the electric field of an infinite plane of charge with surface charge density ps located at the x-y plane. 2. Find the electric field due to a...
For the next six problems, consider a uniformly charged disk of radius R. The total charge on the disk is Q. To find the electric potential and field at a point P (x>0) on the x-axis which is perpendicular to the disk with the origin at the center of the disk, it is necessary to consider the contribution from an infinitesimally thin ring of radius a and width da on the disk, as shown. What is the surface charge density...
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0<x<1 (a) Specify the joint pdf fxy(x,y) and sketch its region of support Ω XY. (b) Determine fxly(x1025). (c) Determine the probability P(X〈2Y). (d) Determine the probability P(X +Y 1)
Problem 2: Show whether the Stoke's theorem is valid for the following function while uniformly distributed charge is contained within a surface with radius R, centered at the origin within xy plane: Problem 2: Show whether the Stoke's theorem is valid for the following function while uniformly distributed charge is contained within a surface with radius R, centered at the origin within xy plane: