Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Joint Density Functions
Transformation of Variables
Jacobians

Formulas

f(x, y) = 2 / (x * y^3) if x ≥ 1 and y ≥ 1
U = XY, V = X / Y
Jacobian Matrix J = [[∂X/∂U, ∂X/∂V], [∂Y/∂U, ∂Y/∂V]]

Theorems

Change of Variables Theorem for Joint Distributions

Suitable Grade Level

University Level (Advanced Probability/Statistics)