Реферат: Теорія імовірностей та математична статистика

Дискрентна вибірка 1,0,-1,2,3,2,3,-1,0,5,4. Результат:

Графіки:

Текст програми (Object Pascal Delphi 4 з застосуванням технології ActiveX):

unit main;

interface

uses

Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs,

Grids, DBGrids, StdCtrls;

type

TForm1 = class(TForm)

StringGrid1: TStringGrid;

Button1: TButton;

Button2: TButton;

ComboBox3: TComboBox;

Label1: TLabel;

Edit1: TEdit;

procedure Button2Click(Sender: TObject);

procedure Button1Click(Sender: TObject);

private

{ Private declarations }

public

{ Public declarations }

end;

var

Form1: TForm1;n:integer; typ:boolean;

implementation

uses Unit2;

{$R *.DFM}

procedure TForm1.Button2Click(Sender: TObject);

begin

close;

end;

procedure TForm1.Button1Click(Sender: TObject);

var i:integer;

begin

i:=30;n:=30;

while (StringGrid1.Cells[i,0]='') do begin

n:=n-1;

i:=i-1;

end;

typ:=true;

if Combobox3.ItemIndex=1 then typ:=false;

Form1.Visible:=false;

Form2.Showmodal;

end;

end.

unit Unit2;

interface

uses

Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs,

StdCtrls, Grids;

type

TForm2 = class(TForm)

StringGrid1: TStringGrid;

Button1: TButton;

Button2: TButton;

Edit1: TEdit;

Edit2: TEdit;

Edit3: TEdit;

Edit5: TEdit;

Label1: TLabel;

Button3: TButton;

Label2: TLabel;

Edit4: TEdit;

Label3: TLabel;

Edit6: TEdit;

Memo1: TMemo;

Label5: TLabel;

Label6: TLabel;

Label7: TLabel;

Edit8: TEdit;

Label8: TLabel;

Edit9: TEdit;

Label9: TLabel;

Edit10: TEdit;

Label10: TLabel;

Edit11: TEdit;

Label4: TLabel;

Edit7: TEdit;

Label11: TLabel;

Edit12: TEdit;

Label12: TLabel;

Edit13: TEdit;

Label13: TLabel;

Edit14: TEdit;

Label14: TLabel;

Edit15: TEdit;

procedure Button2Click(Sender: TObject);

procedure Button1Click(Sender: TObject);

procedure FormActivate(Sender: TObject);

procedure Button3Click(Sender: TObject);

private

{ Private declarations }

public

{ Public declarations }

end;

var

Form2: TForm2; xi,ni,wi:variant;m,r:integer;sx,s,ser:double;

implementation

uses main, Unit3;

{$R *.DFM}

procedure TForm2.Button2Click(Sender: TObject);

begin

halt;

end;

procedure TForm2.Button1Click(Sender: TObject);

begin

Form2.Close;

Form1.Visible:=true;

end;

procedure TForm2.FormActivate(Sender: TObject);

var sn,i,j,k:integer;p,w,v,t:variant;dx,tx:double;

s1,s2,s3:string;

begin

v := VarArrayCreate([0,n], varDouble);

p := VarArrayCreate([0,n], varDouble);

m:=0;

for i:=1 to n do begin

v[i]:=Form1.StringGrid1.Cells[i,0];

p[i]:=Form1.StringGrid1.Cells[i,0];

end;

{sorting}

k:=n;

while k<>0 do begin

for i:=n-1 downto 1 do

if v[i]>v[i+1] then begin

t:=v[i]; v[i]:=v[i+1]; v[i+1]:=t;

end;

k:=k-1;

end;

{об'єм вибірки}

xi:=n;

edit5.Text:=xi;

if typ=true then begin

w := VarArrayCreate([0,n], varDouble);

for i:=1 to n do

w[i]:=Form1.StringGrid1.Cells[i,0];

{об'єм ряду вибірки}

for i:=1 to n do

if w[i]<>-666 then begin

m:=m+1;

if i<>n then

for j:=i+1 to n do

if w[i]=w[j] then

w[j]:=-666;

end;

xi := VarArrayCreate([0,m], varDouble);

ni := VarArrayCreate([0,m], varInteger);

wi := VarArrayCreate([0,m], varDouble);

sn:=0;

sx:=0;

k:=0;

for i:=1 to n do

if v[i]<>-666 then begin

k:=k+1;

xi[k]:=v[i];

ni[k]:=1;

if i<>n then

for j:=i+1 to n do

if xi[k]=v[j] then begin

ni[k]:=ni[k]+1;

v[j]:=-666;

end;

end;

sn:=0;sx:=0;

for i:=1 to m do begin

sn:=sn+ni[i];

sx:=sx+xi[i];

end;

s:=sx/m;

for i:=1 to m do

wi[i]:=ni[i]/sn;

{moda}

t:=ni[1];

for i:=1 to m do

if t<=ni[i] then begin

t:=ni[i];

k:=i;

end;

Edit4.text:='{';

for i:=1 to m do

if t=ni[i] then begin

w:=xi[i];s1:=w;

Edit4.text:=Edit4.Text + s1;

if k<>i then Edit4.Text:=Edit4.Text + ','

else Edit4.Text:=Edit4.Text + '}';

end;

{mediana}

if m mod 2<>0 then begin

t:=(m+1)/2; t:=xi[t];

Edit6.Text:=t;

end

else begin

t:=m/2;k:=t;

t:=xi[k];

s1:=t;

t:=xi[k+1];

s2:=t;

Edit6.Text:='[' + s1 + ',' + s2 + ']';

end;

{Середнє}

ser:=0;

for i:=1 to n do

ser:=ser+p[i];

ser:=ser/n;

t:=ser; Edit15.Text:=t;

{Deviacia}

tx:=0;

for i:=1 to n do

tx:=tx+(p[i]-ser)*(p[i]-ser);

t:=tx;

Edit8.Text:=t;

{Variansa}

if n<>1 then sx:=tx/(n-1);t:=sx;

Edit9.Text:=t;

sx:=0;

{momenty}

for i:=1 to n do {1}

sx:=sx+p[i]-ser;

sx:=sx/n;

t:=sx;

Edit7.Text:=t;

tx:=tx/n;t:=tx; {2}

Edit12.Text:=t;

sx:=0;

for i:=1 to n do {3}

sx:=sx+(p[i]-ser)*(p[i]-ser)*(p[i]-ser);

sx:=sx/n;

t:=sx;

Edit13.Text:=t;

{Assymetrija}

if tx<>0 then sx:=sx/(sqrt(tx)*sqrt(tx)*sqrt(tx));

t:=sx;

Edit10.Text:=t;

sx:=0;

for i:=1 to n do {4}

sx:=sx+(p[i]-ser)*(p[i]-ser)*(p[i]-ser)*(p[i]-ser);

sx:=sx/n;

t:=sx;

Edit14.Text:=t;

{Eksces}

if tx<>0 then sx:=sx/(tx*tx)-3;

t:=tx;

Edit11.Text:=t;

{rozpodil function}

s2:=xi[1]; sx:=0;

Memo1.lines[0]:='0, x<' + s2;

for i:=1 to m-1 do begin

sx:=sx+wi[i];

t:=sx;

s1:=t;

s2:=xi[i];

s3:=xi[i+1];

Memo1.lines[i]:=s1 + ', ' + s2 + '=<x<' + s3;

end;

s2:=xi[m];

Memo1.lines[m]:='1, x>=' + s2;

for i:=1 to m do begin

Form2.StringGrid1.Cells[i,0]:=xi[i];

Form2.StringGrid1.Cells[i,1]:=ni[i];

Form2.StringGrid1.Cells[i,2]:=wi[i];

end;

end

else begin

sx:=v[n]-v[1];

i:=1;

r:=1;

while i<n do begin

i:=2*i;

r:=r+1;

end;

sx:=sx/(r-1)-0.2;

xi := VarArrayCreate([0,r-1], varDouble);

ni := VarArrayCreate([0,r-1], varInteger);

wi := VarArrayCreate([0,r-1], varDouble);

w := VarArrayCreate([0,r-1], varVariant);

xi[1]:=v[1]-0.2; s1:=xi[1];s2:=v[1]+sx;

Form2.StringGrid1.Cells[1,0]:='[' + s1 + ';' + s2 + ')';

xi[r-1]:=v[n]-sx; s1:=xi[r-1];

s2:=v[n]+0.2;

Form2.StringGrid1.Cells[r-1,0]:='[' + s1 + ';' + s2 + ']';

for i:=2 to r-2 do begin

xi[i]:=xi[i-1]+sx; s1:=xi[i]; s2:=xi[i]+sx;

Form2.StringGrid1.Cells[i,0]:='[' + s1 + ';' + s2 + ']';

end;

i:=1;j:=1;

while i<n do begin

if v[i]<xi[j]+sx then begin

ni[j]:=ni[j]+1;

i:=i+1;

end

else if j<=r-1 then j:=j+1;

end;

ni[r-1]:=ni[r-1]+1;

sn:=0;

for i:=1 to r-1 do begin

sn:=sn+ni[i];

Form2.StringGrid1.Cells[i,1]:= ni[i];

end;

for i:=1 to r-1 do begin

w[i]:=Form2.StringGrid1.Cells[i,0];

wi[i]:=ni[i]/sn;

Form2.StringGrid1.Cells[i,2]:= wi[i];

end;

{moda}

t:=ni[1];

for i:=1 to r-1 do

if t<=ni[i] then begin

t:=ni[i];

k:=i;

end;

Edit4.text:='{';

for i:=1 to r-1 do

if t=ni[i] then begin

s1:=xi[i]+sx/2;

Edit4.text:=Edit4.Text + s1;

if k<>i then Edit4.Text:=Edit4.Text + ','

else Edit4.Text:=Edit4.Text + '}';

end;

{mediana}

if r-1 mod 2<>0 then begin

t:=r/2; s1:=w[t];

Edit6.Text:=s1;

end

else begin

t:=(r-1)/2;

s1:=xi[t+1]+sx-sx/2;

s2:=xi[t+1]+sx+sx/2;

Edit6.Text:='[' + s1 + ';' + s2 + ']';

end;

{rozpodil function}

s2:=xi[1]; w[1]:=0;

Memo1.lines[0]:='0, x<' + s2;

for i:=1 to r-1 do begin

w[1]:=w[1]+wi[i];

t:=w[1];