> with(stats):

with(plots):

Areabargraph:=proc(data,xmin,xmax,k)
local sorteddata, dx, lines,graphicslist, f: sorteddata:=[]: dx:=(xmax-xmin)/k: lines:=[]: graphicslist:=[]:
### WARNING: incomplete quoted name; use ` to end the name
sorteddata:=sort(data): if ((op(1,sorteddata)<xmin) or (op(nops(sorteddata),sorteddata)>xmax)) then lprint(`Note: some data
values lie outside the user-defined interval.`) fi: f:=proc(k,sorteddata,xmin,dx,xmax,lines::evaln) local
i,j,currentupperlim,leng,index,counter,result, finallist,q,numb,linelist: finallist:=[]: linelist:=[]: index:=1:
leng:=nops(sorteddata): currentupperlim:=xmin+dx: result:=[]: for q from 1 to leng do if ((op(q,sorteddata)>=xmin) and
(op(q,sorteddata)<=xmax)) then finallist:=[op(finallist),op(q,sorteddata)] fi: od: numb:=nops(finallist): for i from 1 to k
do counter:=0: while ((index<=numb) and (op(index,finallist)<=currentupperlim)) do counter:=counter+1: index:=index+1: od:
result:=[op(result),counter]: currentupperlim:=currentupperlim+dx: od: for j from 1 to k do linelist:=[op(linelist),[xmin +
(j-1)*dx,0]]: linelist:=[op(linelist),[xmin + (j-1)*dx,op(j,result)/(leng*dx)]]: linelist:=[op(linelist),[xmin +
j*dx,op(j,result)/(leng*dx)]]: linelist:=[op(linelist),[xmin + j*dx,0]]: od: lines:=linelist: end:
f(k,sorteddata,xmin,dx,xmax,lines): plot(lines,style=LINE); end:

Warning, the name changecoords has been redefined

> CoinToss:=proc(n)
local L,T,V,i;
T:=[];
V:=0;
L:=[random[empirical[.5,.5]](n)];
for i from 1 to n
do
V:=V+2*(L[i]-3/2);
T:=[op(T),V];
od;
T;
end:

BigCoinToss:=proc(n,m,M)
local L,T,V,i,j;
T:=[];
for j from 1 to m
do;
V:=0;
L:=[random[empirical[.5,.5]](n)];
for i from 1 to n
do
V:=V+2*(L[i]-3/2);
od;
T:=[op(T),V];
od;
lprint(T);
Areabargraph(T,-max(-min(op(T)),max(op(T))),max(-min(op(T)),max(op(T))),M);
end:

> CoinToss(100);

> BigCoinToss(4^2,200,11);

[-2, 2, 2, 2, -2, -8, -8, 4, 8, 0, -2, 2, 0, -2, -4, 0, -2, 0, -2, -2, 2, 0, 0, 2, -2, 0, -8, -6, 2, 4, -8, 2, -4, 0, 2, 4, -4, -2, 4, 4, 4, 4, 4, -2, 0, -2, -6, 2, 2, 4, 6, -2, 4, 4, -4, 0, 0, 4, 4, 8, 4, 2, -2, 2, 4, 4, 6, -6, -2, -4, 2, 2, 0, 2, 4, 2, -4, -6, -4, -4, 0, -4, -2, 4, -2, 2, 6, 0, -2, 4, 8, 0, -8, 0, -2, -4, 0, 0, -2, -2, -4, -6, 2, 4, 4, 4, 0, -2, -6, 0, 2, 0, -2, 4, 0, 0, 2, 4, 2, 4, -2, -10, 8, 4, 6, 4, 2, -2, -4, 4, 2, -2, 2, 0, 6, -6, -4, 0, 0, 0, -2, 10, -2, 6, 4, -4, 10, -4, -6, 0, 4, 6, -2, -2, 6, 4, 8, 10, 2, 0, 6, 2, -2, 2, -2, -4, 8, 4, -2, -2, 0, 2, 2, 4, 8, 0, 0, -4, 2, 2, 0, 6, 2, -4, -6, 2, 6, 4, -6, -6, -2, -4, 0, -2, 2, 2, -6, 8, -6, 2]

> BigCoinToss(9^2,200,11);

[-1, 3, -11, -15, 5, 13, -11, -5, 5, 5, -3, -9, 3, 1, -5, 27, 1, 1, -3, 9, -5, -1, -7, 1, 1, 11, 3, 3, 3, 7, -7, -1, -1, 7, -5, -9, -5, 15, 13, -1, 11, -11, -3, -13, 1, 9, 3, -19, 17, -1, 3, 9, 7, -1, 7, 21, 5, -1, -7, 1, 3, -1, 7, -13, 5, -5, 1, 3, 11, -3, 11, -1, -9, -1, 15, -7, 11, -5, 9, -7, 1, -3, 9, 1, 3, -7, -17, -15, -7, -1, 1, 13, -1, -9, 17, -9, 13, 1, 9, -7, 19, -17, 1, 7, 1, -7, -9, -11, 1, -15, -11, 15, 5, 5, 5, 5, 9, -3, -15, 7, 1, 17, 17, 9, 3, -11, 5, -1, -9, 9, -21, 1, -7, 13, 15, 13, -3, 11, 1, -3, 17, 1, -3, 1, -11, 11, -3, 1, -1, 11, -1, -3, -9, -3, -5, 1, -7, 1, 5, 3, 5, 9, -1, 7, -5, -1, 21, -17, -3, -3, -3, 7, 7, 13, 7, -5, -5, 13, 7, -5, 15, 3, 3, -5, 5, -5, 11, 17, 11, 17, 9, -1, -3, -13, 7, -1, 7, -7, -11, 5]

> BigCoinToss(15^2,200,11);

[1, 13, -7, -17, 25, -3, -13, 9, -5, 1, -29, 7, -13, 9, 3, 1, 15, -7, -27, -9, -1, -11, 11, -11, -5, 29, 1, -11, -11, -19, 27, -1, 19, 15, 1, 17, 27, -19, 21, -5, 11, 35, -1, -31, -1, -1, 7, 21, -13, 3, -19, -15, 9, 17, -5, -23, -17, -9, -25, -3, -13, -17, 1, 11, 5, -17, -21, 5, 19, 13, 19, 15, 11, 13, -13, -7, -13, -5, 5, -13, 21, 13, 13, 3, 17, 3, 11, -9, -31, 11, 1, 33, -21, 11, -7, -3, 51, -3, -11, -1, 9, 21, 5, -9, 7, -3, 1, -5, -11, 19, -3, 15, -1, 1, -7, -1, 9, 3, 1, -31, 7, -9, 1, -19, 21, 25, -11, -9, 5, 7, -21, -9, 9, -13, -7, 3, 11, 3, -13, -5, 3, 5, 25, 11, 1, -21, -7, 5, 21, 13, 9, 11, -19, -13, 3, -7, -27, -13, -23, 19, -15, 11, -15, 17, 13, 7, -11, -3, -13, 7, -13, -27, 11, -13, -11, 21, 27, -5, -17, -1, 5, -19, -27, -7, 1, 15, 29, -11, 7, -19, 7, 15, 9, 1, -5, 9, -7, -5, -1, 9]

> BigCoinToss(21^2,200,11);

[35, -21, 17, -1, -9, -17, -35, 9, 5, -21, 9, 31, -5, -11, -1, -3, -25, 25, -47, -37, 7, -7, 13, -9, -29, 7, -15, 19, 3, 49, 3, -19, -5, -15, -21, -27, -1, 51, 31, 13, -15, -7, 27, 41, 21, 11, -7, -1, 1, -25, -25, 7, -1, 27, -29, 7, -19, -1, 7, 11, 33, 9, 11, 19, -35, -19, 5, -3, -25, -13, -3, -47, -23, 45, 51, -37, -27, 3, -25, 15, 5, -11, -17, 13, -29, -27, 37, 33, 21, -11, 11, -15, -25, 9, -13, 31, 7, -9, 33, 23, -1, 27, 35, -9, 11, -15, 35, -33, 29, -9, 53, -21, -3, -27, -15, 7, -23, -23, 23, 9, -11, -37, -29, -33, 15, 49, -19, -23, -19, 33, -15, -41, 17, -9, 7, -27, 1, -7, -7, -11, 17, 1, 19, -11, 5, 19, 5, -15, -1, -11, -11, -3, 25, 1, -29, -5, 9, -15, -31, -19, -25, 5, 1, -11, 5, 21, 35, -21, 13, 15, 7, 15, -7, -23, 19, -29, -41, 9, 17, 9, 37, -3, -19, -13, -27, -21, -1, 13, -9, 17, -3, -37, -7, 13, 3, -7, 29, -7, 31, 13]

> BigCoinToss(27^2,200,11);

[-49, 11, 25, -31, 5, -27, 9, -3, 1, -33, 53, -29, -49, -3, -35, 41, 29, 35, 37, 11, -5, -15, -35, 27, -39, -31, -7, 31, -25, 15, 27, 9, 23, 7, 29, 11, -27, -51, -23, -43, -55, -13, 13, -25, 1, -29, -1, -5, 1, -9, 15, 19, -3, 21, -11, 21, -7, 17, -37, 71, -39, 25, -81, -3, -3, -31, 1, 45, 37, 41, 9, 31, 7, -25, -13, -13, -57, 41, -25, 49, -23, 37, -9, -1, -11, 11, -19, -15, 21, -27, -11, -3, 7, -41, -3, 15, -9, 17, 11, 21, 39, -23, 13, -29, -17, -55, -3, 1, 23, -1, -27, 29, -19, -11, -61, 31, 7, -13, -5, 35, -1, 17, 21, 1, -33, -39, 49, 15, 5, 21, 37, -25, 15, 53, 35, -7, 45, 19, -3, -17, -45, -17, -1, 5, -15, 53, 49, 31, 15, -25, -51, -9, -5, 33, 17, -15, -19, 29, -5, 5, -39, 25, -15, 31, -5, 19, -23, -7, -15, 5, -49, 9, -1, -15, -21, -27, 29, -43, 19, -11, -5, -49, 21, -13, 9, 15, 7, 35, 59, -7, -43, -5, -3, -7, -27, 23, 15, 19, -37, -25]

> BigCoinToss(33^2,200,11);

[-45, 17, -21, -41, -9, -39, -57, -25, 3, 25, 3, -7, -51, -17, 53, -39, 3, 19, -21, 5, -69, 11, 43, 41, 21, -47, 13, -61, -55, -11, 3, -3, -15, -1, -61, -41, 9, -31, -27, -7, -37, -49, -19, -21, -33, 43, 13, 43, -5, -37, 13, -13, -19, 13, 25, 15, 21, 17, -49, -23, -63, 15, -9, -9, 67, 9, 3, 17, 11, 13, 19, -7, 9, -11, -13, 41, -21, -43, -31, -19, -9, -27, -31, 19, 15, 39, -51, 45, 3, 31, -11, -11, 3, 69, 35, -31, -33, -53, -55, -31, -53, 3, -51, 3, 41, -53, 27, 15, 1, 87, -75, -11, 33, 35, 15, 37, 7, -25, -27, -1, 25, -71, -33, 11, 5, -19, -41, 35, -9, -37, 11, -53, 29, 53, 37, -51, -7, -9, -17, 29, -45, 35, -33, 13, 75, -11, -43, 33, -11, 81, -1, 31, -11, -47, 75, -35, 49, 3, 45, -17, -7, 11, 67, -13, 11, -37, -29, 3, -19, -9, -13, -47, -3, 39, -49, 17, 31, -45, 9, 15, 9, 29, -27, -33, 3, 13, -27, -41, -9, -1, 21, -5, -1, 63, -21, 29, 35, 21, 71, 1]

> BigCoinToss(10,500,9);

[-2, -2, -2, 2, -2, 2, -4, 0, 4, -2, 0, 2, -2, 2, 2, 2, 2, 0, 0, -4, -4, -2, -2, -4, 0, 4, -2, 0, -2, 2, -2, -2, 0, -4, -2, -2, 4, 0, 2, -2, -6, 0, 4, -6, 0, -4, 0, 2, 0, 2, -4, 0, 2, -2, -2, 0, -4, 0, 6, 2, 4, 0, -6, 0, 6, 2, 2, -6, -4, 2, 2, 0, -2, -2, -2, 0, 0, 6, 2, 6, -4, 0, -4, 2, 2, -2, 2, 0, 4, 2, 4, 4, 4, -2, -2, 0, -2, -4, 2, 6, -2, 0, 0, 2, 0, -6, 0, 2, 6, 0, 2, -6, -4, 6, 0, -2, -6, -2, -4, 2, 0, -2, -4, 2, 2, 0, -6, 4, 0, 0, -4, 0, -2, 0, 2, -6, 2, -2, 2, -2, -4, 4, -4, -6, 2, -2, -2, -2, 6, 0, 4, 0, 0, 2, -2, 4, -2, 2, 2, -2, 2, 4, -4, -2, -2, -2, 2, 4, -2, 4, -4, 0, -4, 4, -2, 0, -4, 2, 2, 4, 2, 4, 2, 2, 2, 2, -2, 2, 0, -4, 2, 4, 0, 0, -6, 4, 0, 0, 2, 0, 0, 4, 0, -4, 6, -4, -2, 0, -4, 2, 0, 4, 2, -6, 0, -2, 2, -4, 2, 2, 2, -2, 2, 0, 4, -8, -2, -6, 8, 4, -4, 2, 2, 0, 4, -8, 2, 6, 4, 2, -2, 0, -2, 4, 2, 4, -2, 0, -2, 6, -4, 0, 2, -2, 0, 0, 0, 0, 8, 6, 4, 0, -4, 4, -2, 0, 0, -4, -6, 0, 0, -6, 0, -4, 0, 0, 2, 0, 2, 2, 2, 6, -2, 2, -2, -2, 0, -2, -4, 0, 0, 0, 0, 2, 0, 6, -4, 4, -2, 2, 0, 6, -2, 6, -4, -2, -4, 0, 2, 0, -2, 0, -2, -2, 2, 0, 2, 4, 2, 0, -4, -2, 0, -2, 0, 0, 0, 0, 2, 0, -4, 0, 2, -4, 0, -4, -2, -4, -2, 4, -4, -4, 0, 2, -2, 2, -2, -2, 6, 2, 0, -4, 0, -2, 0, 0, -2, 6, 0, 4, 0, -2, 0, 0, -2, 0, -2, -2, 2, -4, 4, 0, -2, -2, 4, 4, -2, 0, -2, -6, 0, 4, 2, -2, 2, 0, -6, 2, 6, 6, -2, -2, -4, 2, 2, -8, -2, -4, 4, 6, 4, 2, 0, 0, 2, -2, -2, 2, 0, 2, 0, -6, -2, -8, -4, -4, 0, 4, -4, -2, 0, -2, -2, 4, -8, -2, -4, 2, -2, 0, 0, 2, 0, -2, 4, -2, -2, 6, 4, 2, -2, -4, 0, 0, -2, -2, 2, -2, 0, 0, 4, -4, 8, 4, -6, 0, -4, 0, 0, -2, 4, -4, 0, -2, 2, -4, 0, 0, 0, 0, 2, 2, 2, 0, 2, -4, 2, 0, 2, 2, -4, 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, -2, 2, 8, -4, -2, 2, 2, -2, -2]

> BigCoinToss(1000,500,11);

[32, 0, 20, 32, 4, -6, -10, 50, 30, -10, -30, 80, 0, 18, 20, -44, 24, 16, 54, -20, 38, -24, -18, 40, 12, 28, 62, 4, -8, -26, -8, 14, -8, -8, -32, 40, 74, 8, 96, 52, -8, -8, 22, -20, -16, -4, -34, 8, 6, -50, -30, 10, -24, 2, 42, 34, -8, 0, 32, -46, 22, -24, 0, -6, 20, 2, 36, -78, 50, -4, -32, -4, 6, 2, 52, -34, 60, 42, 52, -56, -4, 4, 20, 96, -16, -20, -64, 6, -10, -28, 68, 12, -10, -10, -20, 18, 14, -70, 24, -34, 10, 8, -38, 6, -38, -4, 8, 22, 46, 46, -14, -10, 4, -78, -16, -34, 82, -26, 24, 42, -24, 18, 34, 28, 0, 10, 10, -24, 18, -22, -16, 0, 38, -16, 36, -68, -10, 20, -18, -42, 34, -62, 30, 16, 14, 22, 12, -14, -46, -20, 48, -22, -12, -40, -22, 10, -50, 14, 56, -28, -28, -10, 64, -2, 54, 40, -8, -62, 8, 16, -38, 26, 62, -2, -14, -42, -34, -60, 64, -30, -18, 6, -28, 6, 44, 0, -22, 18, 2, 38, 70, 4, 2, 18, 22, -22, -20, -28, 0, -76, 4, 4, 20, -58, -10, -8, -24, 18, 14, 20, -16, -10, 16, -42, 8, -72, -20, 6, 50, -10, 28, -2, 12, -64, 30, 22, -42, -28, 4, -18, -12, 4, 30, 36, -22, 38, 22, -2, 34, 28, -40, 42, -28, 42, 30, 20, -4, 28, 44, 26, -32, 14, -42, -2, 4, 4, -32, 44, -56, -36, -20, 48, 52, 38, 6, -12, -24, -20, -26, -4, -10, 18, 30, 38, 18, 32, -30, -60, -72, -40, 4, -40, -6, -30, 2, 24, -16, 26, 18, -14, 48, 12, -66, 50, 2, -82, -2, -28, 24, 18, 82, 28, 14, -22, -46, -34, 30, 30, -32, 62, -40, 6, -8, -12, 0, 0, -22, -6, -20, -2, -6, 18, 38, 8, 12, -24, -54, -26, 18, -8, -6, 8, -10, -62, 8, 8, -8, 56, 12, 14, -14, -44, 44, 12, 36, 2, 8, 76, 10, 52, 0, -10, -50, -22, 12, 12, 80, 26, 22, -74, -6, 12, 20, -28, 8, 16, -6, -26, 8, 14, 26, -30, 6, -16, -30, -10, -16, -38, 16, -20, -6, -12, -28, -18, 22, 36, 6, 88, -50, -10, -14, -34, 8, 22, -38, -18, -36, 30, -34, -18, -34, -8, -56, -22, -34, 32, -6, 12, -24, -34, -24, 54, -50, 42, -10, -2, 2, -44, -42, 26, 24, 70, 6, -58, 22, -44, -48, -8, -28, -12, 50, -62, 8, -48, -48, 18, -44, -52, 8, -8, -52, -38, 18, -44, -12, 42, -2, 52, -10, -46, 32, -14, -52, 26, 16, 28, -8, 34, 28, -58, -28, -54, 8, -22, 20, 24, 34, 22, -22, 8, 20, 22, 12, -10, 0, -2, 2, 4, 6, 2, -46, -38, 10, -28, -32, -20, 20, 8, 10, 26, -20, 10, 2, 58, -34, -6, -4, 64, 68, -40]

> BigCoinToss(100,500,11);

[-10, -4, -4, 10, -4, 6, 30, 8, 6, -16, -4, -10, 16, -12, 0, 2, 14, -12, 12, 6, -2, -6, 0, -4, -10, -4, 6, -2, 12, -4, -12, -8, -10, -12, 2, -16, 6, -6, 2, 8, -4, -10, -8, 10, 6, 2, -8, 6, 12, -26, 8, -2, 0, -4, 14, -8, 14, 12, 10, 4, 0, 2, -12, 2, -2, -8, 2, -8, 2, 0, 2, -4, 2, -20, 4, 14, -4, -2, 8, -12, -18, 6, 4, -12, 16, 2, -10, -10, 6, -24, -10, -26, -2, -8, 18, 10, 0, 0, -18, 14, -12, 6, -8, 10, 2, 0, 2, 0, 8, 2, -16, -6, -22, -6, -8, 4, 6, -8, 6, 0, -2, 26, -22, -6, 2, 4, -10, -4, 22, 4, -24, 10, 8, 6, 2, 28, 4, 12, 2, 8, -4, 8, -4, -6, 2, -14, -8, 0, -8, 6, 4, 2, 14, -12, -16, -8, -18, 6, 4, -4, -8, -16, -16, 4, 4, -2, 2, 0, -2, 24, -2, 14, 0, 20, 12, 4, 4, 6, 6, 0, -6, 16, 2, -10, 12, -26, 2, -2, 10, 0, -8, -10, -10, 26, 10, 24, 28, 8, -4, -10, 18, 8, -10, 6, -16, 8, 8, 12, -8, 14, 0, -2, -18, 10, 4, -14, 8, -2, 4, 2, -6, 0, 8, -2, -12, -10, -6, -10, -16, -8, 4, 16, 0, -8, 0, 10, -2, -2, -8, -2, 4, 14, 2, 14, 8, -14, -24, -14, 20, 6, -20, 10, -2, -16, 2, -20, 22, -6, -2, -6, 10, 0, -6, -12, 6, 12, 0, -8, 16, 8, 10, 14, -2, 8, 4, -4, 2, 2, 4, 24, -10, 10, -10, 12, -2, 0, 10, 8, -14, -6, -2, -16, -8, 6, -6, -6, -8, 10, -2, 18, -20, 2, -10, 4, -2, 0, -4, -2, -2, -8, -14, -8, -2, 4, 2, -4, 6, 0, -4, -14, -8, -2, -24, 4, -20, -14, 14, -8, 8, -10, 10, 24, 22, 16, 8, -8, 20, -12, -6, -10, 6, -6, -16, 12, -20, -2, 10, -12, 0, -2, -8, 8, -10, -6, -8, 10, 6, -10, 4, -4, 2, 2, 4, 6, 6, -2, -12, -2, -12, 14, -16, -4, 12, 0, 14, -8, -10, -16, 8, -8, -6, -16, -10, -4, 2, -6, 16, 12, 4, 14, 24, -10, 14, 2, 2, -2, 2, 14, 0, -2, -6, -18, 20, 12, -4, 12, -8, -10, 10, -8, -2, -14, -4, -18, 2, -4, 10, -2, 8, 2, 4, -10, 12, -16, -4, 0, 14, 2, 8, 8, 10, -2, 2, -8, -12, 14, -2, -6, 10, -4, 12, 14, 12, -6, -12, 22, 8, -2, -16, 6, 10, 10, -12, 32, 4, -2, -4, -2, 12, 22, -4, 2, 0, 2, -2, 10, -6, -4, 8, -2, 6, -10, -4, -2, 12, 6, 8, 6, -8, -12, -20, 6, 8, 4, 20, -10, 12, -2, -8, 8, -12, 20, 16, 8, 8, 0, 2, 2, -8, -14]

>