55570c30-8c42-4cd8-96a6-c549c865c937 48 6 9 decimal

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

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

t0 1 time :

n x Pascal n! (k! (n k - (! (* / x (n k -^* (k 0 n sum :

N 5 :

Optimiz => any x p out 1 el 1 : k 2 : i 1 N range out k el i x Pascal : k k 1 + : 21 line for out 41 line :

Optimiz => NONE ... module to expand wrt x^n coefficients k 1 : i 1 N range Triangle k el x p i el parfrac x convert maple : k k 1 + : 21 line for Triangle 31 line

x p 11 x + 1 x 2 x + (* + 1 x 3 x 3 x + (* + (* + 1 x 4 x 6 x 4 x + (* + (* + (* + 1 x 5 x 10 x 10 x 5 x + (* + (* + (* + (* + 61 mat

Triangle 5 el coeffs maple transpose 1414615 mat

Optimiz => NONE C 1 el 1 : k 2 : i 2 N range C k el Triangle i el coeffs maple transpose : k k 1 + : 21 line for C 41 line

Triangle 1 x 1 + x 2^2 x * + 1 + x 3^3 x 2^* + 3 x * + 1 + x 4^4 x 3^* + 6 x 2^* + 4 x * + 1 + 51 mat

C 11112 mat 12113 mat 131314 mat 1414615 mat 51 mat

========================================= =============================================

nB 11210345412052106252721081209451010111112 mat :

n nB 1 col : Y nB 2 col : Ntrial 12 : 31 line

No Normalize n 1 Y rows range Y n el Y n el 252 / : for Y 31 line :

v nB 2 col :

v Max 252

σ Ntrial 112 / - (* 12 / * sqrt : μ Ntrial 2 / : 21 line

PD η 2 σ 2^* π * sqrt : x 012 0.05 range : i 1 x rows range PD i el x i el PD eval : for x η PD * augment 41 line :

x PD x μ σ pdf.Normal :

μ σ 12 mat 6 1.732051 12 mat

bin n No . 10 red plotG :

PD bin 2 1 sys

Cn(m,n): cleaned version from Smath collab m n Cn t 1 m / 1 x m^- 1 x - / (* (n^simplify maple : k 0 : 1 cf t x k coeff maple : cf 0 ≡ break k k 1 + : c k el cf : 21 line if 21 line while c eval 41 line :

b 3015 Cn :

b length 436

x 0 b length 1 - range b length 1 - / eval :

x μ σ PDNormal 1 σ 2 π * sqrt * / e 12 / x μ - σ / (2^* -^* :

scale 1 b Max / : 84.892

xy x b scale * augment :

0.19565 x 0.5 0.07785 PDNormal * xy 2 1 sys

The "Normal distribution" is the limit of an infinite set of binomial samples. We can see from the demo, but I can't etablish the 'σ' relationship ! This demo is fitted "Genfit Minimize". ....... "Genfit PDF Normal.sm" .......

The scaling β2 is the last value of the cumulative integration, to be optimized as it is not exact.

μ 1530 / : 0.5

1 time t0 - 1015 sec *

time 48 sec * ≡

data Σ FD Cumulative Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data xy :

data Σ 4362 el 0.1952

β 2 el data Σ 4362 el : 0 0.1952 21 mat

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data XY :

data Σ 492 el #

0.01178