{"id":233,"date":"2018-12-20T11:21:43","date_gmt":"2018-12-20T11:21:43","guid":{"rendered":"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=233"},"modified":"2018-12-20T11:29:43","modified_gmt":"2018-12-20T11:29:43","slug":"central-limit-theorems-i","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/chapter\/central-limit-theorems-i\/","title":{"rendered":"Central Limit Theorems I"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/KBnImvtRDBg\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<img class=\"aligncenter size-full wp-image-235\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1.jpg\" alt=\"\" width=\"1269\" height=\"1417\" \/> <img class=\"aligncenter size-full wp-image-236\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2.jpg\" alt=\"\" width=\"1305\" height=\"1525\" \/> <img class=\"aligncenter size-full wp-image-237\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3.jpg\" alt=\"\" width=\"1289\" height=\"1533\" \/> <img class=\"aligncenter size-full wp-image-238\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4.jpg\" alt=\"\" width=\"969\" height=\"323\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Central Limit Theorems I<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/KBnImvtRDBg\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-242\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1.jpg\" alt=\"\" width=\"1169\" height=\"755\" \/>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/KBnImvtRDBg\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-235\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1.jpg\" alt=\"\" width=\"1269\" height=\"1417\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1.jpg 1269w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1-269x300.jpg 269w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1-768x858.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1-917x1024.jpg 917w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1-65x73.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1-225x251.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-1-350x391.jpg 350w\" sizes=\"auto, (max-width: 1269px) 100vw, 1269px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-236\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2.jpg\" alt=\"\" width=\"1305\" height=\"1525\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2.jpg 1305w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2-257x300.jpg 257w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2-768x897.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2-876x1024.jpg 876w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2-65x76.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2-225x263.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-2-350x409.jpg 350w\" sizes=\"auto, (max-width: 1305px) 100vw, 1305px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-237\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3.jpg\" alt=\"\" width=\"1289\" height=\"1533\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3.jpg 1289w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3-252x300.jpg 252w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3-768x913.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3-861x1024.jpg 861w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3-65x77.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3-225x268.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-3-350x416.jpg 350w\" sizes=\"auto, (max-width: 1289px) 100vw, 1289px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-238\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4.jpg\" alt=\"\" width=\"969\" height=\"323\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4.jpg 969w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4-300x100.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4-768x256.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4-65x22.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4-225x75.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236523CentralLimitTheorems-1-4-350x117.jpg 350w\" sizes=\"auto, (max-width: 969px) 100vw, 969px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Central Limit Theorems I<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/KBnImvtRDBg\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-242\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1.jpg\" alt=\"\" width=\"1169\" height=\"755\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1.jpg 1169w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1-300x194.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1-768x496.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1-1024x661.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1-65x42.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1-225x145.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522236530CentralLimitTheorems-1_Ref-1-1-350x226.jpg 350w\" sizes=\"auto, (max-width: 1169px) 100vw, 1169px\" 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