- #1
rabbed
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If I have the following relations:
X = sqrt(1-V^2)*cos(U)
Y = sqrt(1-V^2)*sin(U)
Z = V
where (-pi < U < pi) and (-1 < V < 1) are independent random variables, both with uniform distributions.
How do I use the CDF method to find X_pdf(x)?
X_pdf(x) =
X_cdf'(x) =
( P( X < x ) )' =
( P( sqrt(1-V^2)*cos(U) < x ) )' = ?
X = sqrt(1-V^2)*cos(U)
Y = sqrt(1-V^2)*sin(U)
Z = V
where (-pi < U < pi) and (-1 < V < 1) are independent random variables, both with uniform distributions.
How do I use the CDF method to find X_pdf(x)?
X_pdf(x) =
X_cdf'(x) =
( P( X < x ) )' =
( P( sqrt(1-V^2)*cos(U) < x ) )' = ?