Suppose that (X, Y) is uniformly distributed on the following right half disk. This half disk...
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.
Show the random variables X and Y are independent, or not independent Find the joint cdf given the joint pdf below Suppose that (X, Y) is uniformly distributed over the region defined by 0 sys1-x2 and -1sx 4 Therefore, the joint probability density function is, 0; Otherwise Suppose that (X, Y) is uniformly distributed over the region defined by 0 sys1-x2 and -1sx 4 Therefore, the joint probability density function is, 0; Otherwise
10. Suppose (X, Y) is uniformly distributed over the disk 2 + y 36. Then 10. Suppose (X, Y) is uniformly distributed over the disk 2 + y 36. Then
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...
Problem 1. (12 Points) A point is uniformly distributed within the disk of radius 1. That is, its density is (a) find the probability that its distance from the origin is less than k, 0 Sk1 (b) determine P(x<Y). (c) determine P(X +Y < 0.5)
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0
5. Let (X, Y) be a uniformly distributed random point on the quadrilateral D with vertices (0,0), (2,0),(1,1), (0,1) Uniformly distributed means that the joint probability density function of X and Y is a constant on D (equal to 1/area(D)). (a) Do you think Cov(X, Y) is positive, negative, or zero? Can you answer this without doing any calculations? (b) Compute Cov(X, Y) and pxyCorr(X, Y)
Need help with question 2 (not question 1) 1. Suppose that (X,Y) is uniformly distributed over the region {(x, y): 0 < \y< x < 1}. Find: a) the joint density of (X, Y); b) the marginal densities fx(x) and fy(y). c) Are X and Y independent? d) Find E(X) and E(Y). 2. Repeat Exercise 1 for (X,Y) with uniform distribution over {(x, y): 0 < \x]+\y< 1}.