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Question: Trouble Multiplying Random Variables

Question:Trouble Multiplying Random Variables

JoyDivisionMan 55 Maple 2025
pdf statistics
6 hours ago
1

I have two random variables:  x and y.  I want to multiply them and get the resulting Probability Density Function, z.  If you look below, Example 1 works as expected.  When I try Example 2, however, I get disappointing results.

Clearly, Example 2 involves nonzero lower boundaries, which is messing me up.  Does anyone have any suggestions for Example 2?

Example 1
> 

with(Statistics)
> 

x := RandomVariable(Uniform(0, 1))

_R

 (1)
> 

y := RandomVariable(Uniform(0, 2))

_R0

 (2)
> 

z = PDF(x*y, t)

z = piecewise(t < 0, 0, t <= 2, (1/2)*ln(2)-(1/2)*ln(t), 2 < t, 0)

(3)

 

 

Example 2

> 

x := RandomVariable(Uniform(1, 2))

_R1

 (4)
> 

y := RandomVariable(Uniform(2, 3))

_R2

 (5)
> 

z := PDF(x*y, t)

int(piecewise(_t < 1, 0, _t < 2, 1, 2 <= _t, 0)*piecewise(t/_t < 2, 0, t/_t < 3, 1, 0)/abs(_t), _t = -infinity .. infinity)

 (6)
 

NULL

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