A two dimensional non-negative continuous random variable (X, Y) has the joint density f(x, y) = begincases 4xye^-(x^2+y^2); & x ge 0, y ge 0 0; & otherwise endcases. Let T^2 = X^2 + Y^2 such that 0 le (x^2+y^2) < infty. The density function of T is given by:

Q52Section I (Objective (Q1–Q80))52 of 80

Distribution Theory — density of radial distance

A two dimensional non-negative continuous random variable $(X, Y)$ has the joint density $f(x, y) = \begin{cases} 4xye^{-(x^2+y^2)}; & x \ge 0, y \ge 0 \ 0; & \text{otherwise} \end{cases}$ . Let $T^2 = X^2 + Y^2$ such that $0 \le (x^2+y^2) < \infty$ . The density function of $T$ is given by:

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