{"id":390,"date":"2018-12-20T10:28:27","date_gmt":"2018-12-20T10:28:27","guid":{"rendered":"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=390"},"modified":"2018-12-20T12:32:45","modified_gmt":"2018-12-20T12:32:45","slug":"characteristic-functions-ii","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/chapter\/characteristic-functions-ii\/","title":{"rendered":"Characteristic Functions II"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/ziasmBcNZTo\" 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&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-391\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-113.png\" alt=\"\" width=\"439\" height=\"463\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-392\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-114.png\" alt=\"\" width=\"437\" height=\"550\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-393\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-115.png\" alt=\"\" width=\"471\" height=\"550\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-394\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-116.png\" alt=\"\" width=\"434\" height=\"531\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-395\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-117.png\" alt=\"\" width=\"372\" height=\"553\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-396\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-118.png\" alt=\"\" width=\"447\" height=\"552\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-397\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-119.png\" alt=\"\" width=\"478\" height=\"250\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Characteristic Functions II<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/ziasmBcNZTo\" 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\nReferences\r\n<ol>\r\n \t<li>TM Apostol: Mathematical Analysis.<\/li>\r\n \t<li>AK Basu: Measure Theory and Probability.<\/li>\r\n \t<li>P Billingsley: Probability and Measure.<\/li>\r\n \t<li>KL Chung: A Course in Probability Theory.<\/li>\r\n \t<li>W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\r\n \t<li>AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\r\n \t<li>E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\r\n \t<li>E Parzen: Modern Probability Theory and its Applications.<\/li>\r\n \t<li>RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\r\n \t<li>W Rudin: Principles of Mathematical Analysis<\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/ziasmBcNZTo\" 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>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-391\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-113.png\" alt=\"\" width=\"439\" height=\"463\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-113.png 439w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-113-284x300.png 284w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-113-65x69.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-113-225x237.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-113-350x369.png 350w\" sizes=\"auto, (max-width: 439px) 100vw, 439px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-392\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-114.png\" alt=\"\" width=\"437\" height=\"550\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-114.png 437w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-114-238x300.png 238w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-114-65x82.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-114-225x283.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-114-350x441.png 350w\" sizes=\"auto, (max-width: 437px) 100vw, 437px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-393\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-115.png\" alt=\"\" width=\"471\" height=\"550\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-115.png 471w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-115-257x300.png 257w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-115-65x76.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-115-225x263.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-115-350x409.png 350w\" sizes=\"auto, (max-width: 471px) 100vw, 471px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-394\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-116.png\" alt=\"\" width=\"434\" height=\"531\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-116.png 434w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-116-245x300.png 245w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-116-65x80.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-116-225x275.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-116-350x428.png 350w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-395\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-117.png\" alt=\"\" width=\"372\" height=\"553\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-117.png 372w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-117-202x300.png 202w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-117-65x97.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-117-225x334.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-117-350x520.png 350w\" sizes=\"auto, (max-width: 372px) 100vw, 372px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-396\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-118.png\" alt=\"\" width=\"447\" height=\"552\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-118.png 447w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-118-243x300.png 243w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-118-65x80.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-118-225x278.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-118-350x432.png 350w\" sizes=\"auto, (max-width: 447px) 100vw, 447px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-397\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-119.png\" alt=\"\" width=\"478\" height=\"250\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-119.png 478w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-119-300x157.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-119-65x34.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-119-225x118.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-119-350x183.png 350w\" sizes=\"auto, (max-width: 478px) 100vw, 478px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Characteristic Functions II<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/ziasmBcNZTo\" 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>References<\/p>\n<ol>\n<li>TM Apostol: Mathematical Analysis.<\/li>\n<li>AK Basu: Measure Theory and Probability.<\/li>\n<li>P Billingsley: Probability and Measure.<\/li>\n<li>KL Chung: A Course in Probability Theory.<\/li>\n<li>W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\n<li>AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\n<li>E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\n<li>E Parzen: Modern Probability Theory and its Applications.<\/li>\n<li>RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\n<li>W Rudin: Principles of Mathematical Analysis<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":27,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["mr-samopriya-basu"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-390","chapter","type-chapter","status-publish","hentry","contributor-mr-samopriya-basu"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/390","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":1,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/390\/revisions"}],"predecessor-version":[{"id":398,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/390\/revisions\/398"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/390\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/media?parent=390"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapter-type?post=390"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/contributor?post=390"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/license?post=390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}