|
Truck with
truncated Gaussian sacks
Simulates the weight of a truck* load of random no.
of sacks with random weights. |
|
|
| Sacks, n |
|
No. of sacks: min, max,
pout. • |
| Mean of n |
(of true Gaussian) |
Give μ of original, true Gaussian (ignored if not). |
| Weight, w |
t (Br. 'tonne', Am. 'metric ton') |
Weight of sack: μ, σ,
of (true) Gaussian. • |
| Trials, repeatability |
10^ |
No. of trucks simulated, repeatability. • |
| wleft, wright |
t (automatic if 0, 0) |
Limits for the graph abscissae. • |
| Show values |
|
Shows the graph coordinates. |
Simulates the weight of a truck loaded with n,
discrete truncated Gaussian,
sacks weighing w,
Gaussian, each. The total weight,
W = ∑i wi,
i = 1..n, depends on the number of summands
and the individual values. A "reasonable" interval is, thus,
sought for W. (The basis problem addresses a nominal 10 t load.)
(Truncated.xls Gaussian)
If the limits for the graph abscissae are given equal, say,
x, the range will be ±|x| σW.
[Gut, 2005, p 83] With finite means,
E(SN) = E(N) E(X); and with finite variances,
Var(SN) = E(N) Var(X) +
Var(N) E(X)². (Notice the dimensional coherence.)
* "Lorry" may be the Br. Eng. word for "truck".
|
| References: |
Plate: TruckWithTruncGauss |
• Search "random number of random variables".
• [Gut, 2005, p 83], [Thompson], [Ross, 1988], [Ross, 2006].
• Patel, Jagdish, and
Campbell Read, 1996 (1982), "Handbook of the normal distribution", Marcel Dekker,
New York (NY). (ISBN:0-8247-9342-0,
G'b p 33)
• Robbins, Herbert,
"The asymptotic distribution of the sum of a random number of random variables",
Bull. Amer. Math. Soc., 1948, 1151–1161 .pdf (=).
• Virtual
laboratories in Prob & Stat, Univ. Alabama in Huntsville.
• 1746-05-09: Monge, Gaspard (1818-07-28). |
