here P(0<X<2 and 0 <y<3) =(area covered with square of area from 0<X<2 and 0 <y<3) /area of total disk =(2*3)/(*62) =6/(36*) =1/(6)
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
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.
3. [10 pts.] Suppose r.v. y is uniformly distributed over (0,27) i.e. f*() = 1/2, for 0 <o<27 and 0 elsewhere. Consider the following r.v.'s: X = cos y and Y = siny. a. Prove that X and Y are orthogonal. b. Prove that X and Y are uncorrelated.
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}.
Suppose that Y=cos(X), where X is uniformly distributed over the interval [0, 2Pi]. Determine the pdf of the random variable Y.
If X is uniformly distributed over (0,2) and Y is exponentially distributed with parameter λ = 2. Also X and Y are independent, find the PDF of Z = X+Y.
Electric charge is distributed over the disk x^2+y^2≤12 so that the charge density at (x,y) is σ(x,y)=7+x^2+y^ σ(x,y)=7+x^2+y^2 coulombs per square meter. Find the total charge on the disk.
Problem 3: Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of Y. Indicate the range for which it applies. b. (10 points) What is the expected value of Y 0 し( 4 4 Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of...