Let (X, Y, Z) be independent standard normal random variables. Let (, , R) be the corresponding
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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
x = rsinφcosθ, y = rsinφsinθ, z = rcosφ,
for 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π, and r > 0. Find the joint density of (Φ, Θ, R) and the marginal density of R.
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We have x r sin cos y r sin sin z r cos ...View the full answer
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