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Question: Density Function from Multiplying Random Variables

Question:Density Function from Multiplying Random Variables

JoyDivisionMan 50 Maple 2023
statistics statistics density
4 hours ago
0

I am interested in determining the density function which results from multiplying two random variables.  I have read about the Mellin Transformation, but I just end up confused.  I have two random variables:  f[1], which is nonzero on the 0 < t < 2 interval, and f[2], which is nonzero on the 0 < t < 1 interval.  Of course, both of these random variables sum to one when evaluated.

Any thoughts on how I can obtain the density function for this?  My work is below.

> 

restart
> 

with(Statistics)
> 

f[1] := piecewise(t <= 0, 0, 0 < t and t < 2, 1/(Pi*sqrt(1-(1-t)^2)), t >= 2, 0)

piecewise(t <= 0, 0, 0 < t and t < 2, 1/(Pi*(1-(1-t)^2)^(1/2)), 2 <= t, 0)

> 

f[2] := piecewise(t <= 0, 0, 0 < t and t < 1, 2*t, t >= 1, 0)

piecewise(t <= 0, 0, 0 < t and t < 1, 2*t, 1 <= t, 0)


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