Requires knowledge of three-dimensional determinants

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(This exercise requires knowledge of three-dimensional determinants.) Let (X, Y, Z) be independent standard normal random variables. Let (Φ, Θ, R) be the corresponding spherical coordinates. The correspondence between rectangular and spherical coordinates is given by

for 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π, and r > 0. Find the joint density of (Φ, Θ, R) and the marginal density of R.

Reference no: EM131107041

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