3. Let G = 10, 112. Design and implement an algorithm for the visualization of the harmonic measure on JG for any initial value x € G and to solve the corresponding Dirichlet problem.
3. Let G = 10, 112. Design and implement an algorithm for the visualization of the harmonic measure on JG for any initial value x € G and to solve the corresponding Dirichlet problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3 ONLY.
![3. Let G =]0, 12. Design and implement an algorithm for the visualization of the harmonic measure
on JG for any initial value x € G and to solve the corresponding Dirichlet problem.
4. a) Consider a d-dimensional random vector X whose distribution is symmetric with respect to
μ€ Rd, and a function f: Rd → R such that f(X) is square-integrable. Show that
0² (Y)</0² (Y) → Cov(f(X), f(2μ-X)) <0
for Y = f(X) and Ỹ = fg (X).
b) Suppose that d = 1. Show that o²(Ỹ) <0²(Y), if ƒ is strictly monotone.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1e1b415-86bd-4a44-8122-cfbfb1e8f6ee%2F3dffaf03-c1a9-48e7-8df1-d344aa3068f5%2F0incvs5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let G =]0, 12. Design and implement an algorithm for the visualization of the harmonic measure
on JG for any initial value x € G and to solve the corresponding Dirichlet problem.
4. a) Consider a d-dimensional random vector X whose distribution is symmetric with respect to
μ€ Rd, and a function f: Rd → R such that f(X) is square-integrable. Show that
0² (Y)</0² (Y) → Cov(f(X), f(2μ-X)) <0
for Y = f(X) and Ỹ = fg (X).
b) Suppose that d = 1. Show that o²(Ỹ) <0²(Y), if ƒ is strictly monotone.
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