<p> Utilities </p>

7241ded1-b1f5-4737-aeef-c10b27acc674 15 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

<p> Utilities </p>

M Min Max Scale Max Min - (M M min - M max M min - 106 -^+ / (* Min + :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

size min max vx Hist Paul W. MCD 11 => Smath vx last vx rows : numbins max min - size / : hist numbins el 0 : i 1 numbins range bin_mid i el i 1 + (size * size 2 / - : j 1 vx last range i size * vx j el ≤ (i 1 + (size * < hist i el hist i el 1 + : N/A if for 21 line for bin_mid hist vx last / augment 61 line :

vx vy char size clr plotG n vx length : plot vx 1 el vy 1 el char size clr augment : i 2 n range plot plot vx i el vy i el char size clr augment stack : for plot 41 line :

length 100 :

Cols 40 :

The S _j,1 stacks the 40 nested cols.

The ΣS sums the 40 nested cols.

As given [100, 40], noise is "normal"

............. [100, 1 ], noise is "uniform"

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length of 'M': user M length Cols Random :

Central Theorem Limit:
normal random for 30 ≤ cols rn j 1 M cols range S j 1 el M j col : for S sum 21 line eval :

μ rn Mean : 19.8053

rn max 24.5991

rn rn 0 μ Scale :

scale 1 :

rnd scale rn Floor μ / * :

i 1 M rows range :

μ rnd Mean : σ rnd StdDev : 21 mat 0.4701 0.1932 21 mat

½noise 0.5 - rnd + :

'rnd => vector of user scaled normal random

i rnd augment 0.0125 BarSize 1 1 sys

User ½ noise to superpose on function

i ½noise augment 0.0125 BarSize

bin 10 : size 1 bin / : min 0 : max 1 : 41 line

vy rnd sort : h size min max vy Hist : 21 line

μ rnd Mean : σ rnd StdDev : 21 mat 0.4701 0.1932 21 mat

h 0.0125 BarSize 1 1 sys

h 0.15 0.03 0.25 0.09 0.35 0.15 0.45 0.3 0.55 0.5 0.65 0.7 0.75 0.88 0.85 0.96 0.95 0.98 1.05 1102 mat

Transport in => Stat Histogram Code Genfit

h => XY

β 2 el β 1 el 2 π * sqrt * / 12 / x 2 μ * - β 1 el / (2^* - exp *

2 μ * 0.9402