Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 361312 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0846 1210120 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0846 1210120 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1805 4107928 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1822 4135592 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1832 4153304 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1835 4184336 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1848 4207056 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1848 4207056 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.3435 5002720 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.3466 5103704 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.3472 5124632 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3604 5332992 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.3605 5333248 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182 Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0001 361312 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0846 1210120 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0846 1210120 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1805 4107928 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1822 4135592 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1832 4153304 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1835 4184336 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1848 4207056 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1848 4207056 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.3435 5002720 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.3466 5103704 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.3472 5124632 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.5413 13006136 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.5415 13006536 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.5415 13006536 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.5418 13014784 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.5425 13016520 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.5434 13049568 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.5434 13049968 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.5435 13050048 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

Poisson Cumulative Distribution Tables

The table below gives the probability of that a Poisson random variable X with mean = λ is less than or equal to x.

λ =

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

x= 0

0.9048

0.8187

0.7408

0.6703

0.6065

0.5488

0.4966

0.4493

0.4066

0.3679

0.3012

0.2466

0.2019

0.1653

1

0.9953

0.9825

0.9631

0.9384

0.9098

0.8781

0.8442

0.8088

0.7725

0.7358

0.6626

0.5918

0.5249

0.4628

2

0.9998

0.9989

0.9964

0.9921

0.9856

0.9769

0.9659

0.9526

0.9371

0.9197

0.8795

0.8335

0.7834

0.7306

3

1.0000

0.9999

0.9997

0.9992

0.9982

0.9966

0.9942

0.9909

0.9865

0.9810

0.9662

0.9463

0.9212

0.8913

4

1.0000

1.0000

1.0000

0.9999

0.9998

0.9996

0.9992

0.9986

0.9977

0.9963

0.9923

0.9857

0.9763

0.9636

5

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9998

0.9997

0.9994

0.9985

0.9968

0.9940

0.9896

6

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9997

0.9994

0.9987

0.9974

7

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9997

0.9994

8

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

9

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

λ =

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.5

5.0

5.5

x = 0

0.1353

0.1108

0.0907

0.0743

0.0608

0.0498

0.0408

0.0334

0.0273

0.0224

0.0183

0.0111

0.0067

0.0041

1

0.4060

0.3546

0.3084

0.2674

0.2311

0.1991

0.1712

0.1468

0.1257

0.1074

0.0916

0.0611

0.0404

0.0266

2

0.6767

0.6227

0.5697

0.5184

0.4695

0.4232

0.3799

0.3397

0.3027

0.2689

0.2381

0.1736

0.1247

0.0884

3

0.8571

0.8194

0.7787

0.7360

0.6919

0.6472

0.6025

0.5584

0.5152

0.4735

0.4335

0.3423

0.2650

0.2017

4

0.9473

0.9275

0.9041

0.8774

0.8477

0.8153

0.7806

0.7442

0.7064

0.6678

0.6288

0.5321

0.4405

0.3575

5

0.9834

0.9751

0.9643

0.9510

0.9349

0.9161

0.8946

0.8705

0.8441

0.8156

0.7851

0.7029

0.6160

0.5289

6

0.9955

0.9925

0.9884

0.9828

0.9756

0.9665

0.9554

0.9421

0.9267

0.9091

0.8893

0.8311

0.7622

0.6860

7

0.9989

0.9980

0.9967

0.9947

0.9919

0.9881

0.9832

0.9769

0.9692

0.9599

0.9489

0.9134

0.8666

0.8095

8

0.9998

0.9995

0.9991

0.9985

0.9976

0.9962

0.9943

0.9917

0.9883

0.9840

0.9786

0.9597

0.9319

0.8944

9

1.0000

0.9999

0.9998

0.9996

0.9993

0.9989

0.9982

0.9973

0.9960

0.9942

0.9919

0.9829

0.9682

0.9462

10

1.0000

1.0000

1.0000

0.9999

0.9998

0.9997

0.9995

0.9992

0.9987

0.9981

0.9972

0.9933

0.9863

0.9747

11

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9996

0.9994

0.9991

0.9976

0.9945

0.9890

12

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9997

0.9992

0.9980

0.9955

13

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9997

0.9993

0.9983

14

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9998

0.9994

15

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9998

16

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

17

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

λ =

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

11.0

10.0

12.0

14.0

15.0

x = 0

0.0025

0.0015

0.0009

0.0006

0.0003

0.0002

0.0001

0.0001

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

1

0.0174

0.0113

0.0073

0.0047

0.0030

0.0019

0.0012

0.0008

0.0005

0.0002

0.0005

0.0001

0.0000

0.0000

2

0.0620

0.0430

0.0296

0.0203

0.0138

0.0093

0.0062

0.0042

0.0028

0.0012

0.0028

0.0005

0.0001

0.0000

3

0.1512

0.1118

0.0818

0.0591

0.0424

0.0301

0.0212

0.0149

0.0103

0.0049

0.0103

0.0023

0.0005

0.0002

4

0.2851

0.2237

0.1730

0.1321

0.0996

0.0744

0.0550

0.0403

0.0293

0.0151

0.0293

0.0076

0.0018

0.0009

5

0.4457

0.3690

0.3007

0.2414

0.1912

0.1496

0.1157

0.0885

0.0671

0.0375

0.0671

0.0203

0.0055

0.0028

6

0.6063

0.5265

0.4497

0.3782

0.3134

0.2562

0.2068

0.1649

0.1301

0.0786

0.1301

0.0458

0.0142

0.0076

7

0.7440

0.6728

0.5987

0.5246

0.4530

0.3856

0.3239

0.2687

0.2202

0.1432

0.2202

0.0895

0.0316

0.0180

8

0.8472

0.7916

0.7291

0.6620

0.5925

0.5231

0.4557

0.3918

0.3328

0.2320

0.3328

0.1550

0.0621

0.0374

9

0.9161

0.8774

0.8305

0.7764

0.7166

0.6530

0.5874

0.5218

0.4579

0.3405

0.4579

0.2424

0.1094

0.0699

10

0.9574

0.9332

0.9015

0.8622

0.8159

0.7634

0.7060

0.6453

0.5830

0.4599

0.5830

0.3472

0.1757

0.1185

11

0.9799

0.9661

0.9467

0.9208

0.8881

0.8487

0.8030

0.7520

0.6968

0.5793

0.6968

0.4616

0.2600

0.1848

12

0.9912

0.9840

0.9730

0.9573

0.9362

0.9091

0.8758

0.8364

0.7916

0.6887

0.7916

0.5760

0.3585

0.2676

13

0.9964

0.9929

0.9872

0.9784

0.9658

0.9486

0.9261

0.8981

0.8645

0.7813

0.8645

0.6815

0.4644

0.3632

14

0.9986

0.9970

0.9943

0.9897

0.9827

0.9726

0.9585

0.9400

0.9165

0.8540

0.9165

0.7720

0.5704

0.4657

15

0.9995

0.9988

0.9976

0.9954

0.9918

0.9862

0.9780

0.9665

0.9513

0.9074

0.9513

0.8444

0.6694

0.5681

16

0.9998

0.9996

0.9990

0.9980

0.9963

0.9934

0.9889

0.9823

0.9730

0.9441

0.9730

0.8987

0.7559

0.6641

17

0.9999

0.9998

0.9996

0.9992

0.9984

0.9970

0.9947

0.9911

0.9857

0.9678

0.9857

0.9370

0.8272

0.7489

18

1.0000

0.9999

0.9999

0.9997

0.9993

0.9987

0.9976

0.9957

0.9928

0.9823

0.9928

0.9626

0.8826

0.8195

19

1.0000

1.0000

1.0000

0.9999

0.9997

0.9995

0.9989

0.9980

0.9965

0.9907

0.9965

0.9787

0.9235

0.8752

20

1.0000

1.0000

1.0000

1.0000

0.9999

0.9998

0.9996

0.9991

0.9984

0.9953

0.9984

0.9884

0.9521

0.9170

21

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9998

0.9996

0.9993

0.9977

0.9993

0.9939

0.9712

0.9469

22

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9997

0.9990

0.9997

0.9970

0.9833

0.9673

23

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9995

0.9999

0.9985

0.9907

0.9805

24

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9998

1.0000

0.9993

0.9950

0.9888

25

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

1.0000

0.9997

0.9974

0.9938

26

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9987

0.9967

27

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9994

0.9983

28

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9997

0.9991

29

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9996

30

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9998

31

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

32

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

 

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