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Uniform split of a random total

Let

X \geq 0

have density

g

, let

U

be independent and uniform on

[0, 1]

, and set

Y = X U, Z = X (1 - U) .

Then

f_{Y, Z} (y, z) = \frac{g ( y + z )}{y + z} 1_{{y, z \geq 0}}, f_{Y} (y) = f_{Z} (y) = \int_{y}^{\infty} \frac{g ( t )}{t} d t .

Table of contents 73 1
- Exponential characterization by a uniform random split Uniform split of a random total 49

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