|
Weight of truck
with sacks Simulates the weight of a truck* load of
random no. of sacks with random weights. |
|
|
| Sacks |
|
No. of sacks: n and p of binomial. • |
| Weight |
t (Br. 'tonne', Am. 'metric ton') |
Weight of sack: μ, σ, of 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 sacks weighing
w each, both these numbers being random variables, here
n binomial and w Gaussian. (For n,
a better distribution than binomial should be used.) 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.
Binomial.xls)
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".
Example: Nixe (Conservas Garavilla, S. A.),
'mejillones en escabeche' (bar code 2005-5486): can with "13 to 18" units,
capacidad 120 mL, peso neto 111 g, p. escurrido, 69 g
(172 kcal / 100-g). |
| References: |
Plate: TruckWithSacks |
• Search "random number of random variables".
• [Gut, 2005, p 83],
[Thompson],
[Ross, 1988],
[Ross, 2006].
• Robbins, Herbert,
"The asymptotic distribution of the sum of a random number of random variables",
Bull. Amer. Math. Soc., 1948 (54), 1151–1161 .pdf (=).
• Virtual
laboratories in Prob & Stat, Univ. Alabama in Huntsville.
• Weisstein, Eric W., "Binomial Distribution".
From MathWorld—A Wolfram Web Resource.
• 1495-04-16: Apianus, Petrus, birthday. |
