Draws 3 "Monte Carlo" simulated curves:
for the 2 Gaussian variables (summands),
X1 and X2;
and for the sum, X = X1 + X2.
It can be verified (as stated theoretically) that
(a) the sum also is Gaussian, (b) with parameters:
μ = μ1 + μ2 and
σ = √(σ1² +
σ2²) (from
σ² =
σ1² + σ2²).
Other suggested data sets (μ, σ):
34, 0.33 / 66, 0.56;
10, 1 / 11, 1;
10, 0.5 / 10, 1.2;
10, 3 / 20, 4 .
[Pythagorean triples: (3, 4, 5), (5, 12, 13), (7, 24, 25),
(8, 15, 17)...] |
• Weisstein, "Normal sum distribution". From MathWorld—a
Wolfram web resource.
• B. Franco or
here
• Search Monte
Carlo method...
• Normal distribution
(Wikipedia) • "Gaussian or Normal
distribution ?" (Dept. of Computer Sci., Princeton U.).
• Gorard, Stephen, 2004,
Revisiting
a 90-year-old debate: the advantages of the mean deviation, British
Educational Research Association Annual Conference, 16–18 Sep.
(Univ. of York).
• Weisstein, "Pythagorean triple".
From MathWorld—a Wolfram web resource.
• 1873-09-13: Carathéodory, Constantin
(1950-02-02). |
