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Product of two uniforms
Draws (analytical) curves for the pdf of a product of two given uniform variables.
2024.Nov.25 05:12:46
a, b Limits, a < x < b, for the 1.st variable.
c, d Limits, c < y < d, for the 2.nd variable. •
  The graph presupposes that positive values have been given.
Show values Shows the curve coordinates.

Draws the graph of  fZ  for the variable Z = XY.  Of course, it is ac < Z  <bd.

Giving only integer values for the parameters avoids issues of continuity in the graph.

The standard problem (above) yields case 1 (see the resolution by Glen et al. [2004]).  To obtain the other cases, it is suggested: d = 15, and 18.  With d = 6, an almost intuitive result is obtained.

This is so confusing a problem if solved analytically that Monte Carlo simulation would be a safer alternative.

References: Plate: Produnifs

• Glen, A. G., L. M. Leemis, J. H. Drew, 2004, "Computing the distribution of the product of two continuous random variables", Computational Statistics & Data Analysis, 44, pp 451−464.

• 1535-11-01: Della Porta, Giambattista († 1615-02-04, 79 yrs.).

 
 
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Created: 2003-11-01 — Last modified: 2021-07-15