{"id":558,"date":"2021-10-04T14:19:00","date_gmt":"2021-10-04T12:19:00","guid":{"rendered":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/?page_id=558"},"modified":"2024-08-29T22:24:27","modified_gmt":"2024-08-29T20:24:27","slug":"pc","status":"publish","type":"page","link":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/teaching-materials\/pc\/","title":{"rendered":"Probability Calculus"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Winter semester 2021\/2022<\/h2>\n\n\n\n<p><a href=\"#lectures\">Lectures<\/a> &#8212; <a href=\"#classes\">Classes<\/a> &#8212; <a href=\"#homework\">Homework<\/a> &#8212; <a href=\"#other\">Other<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"lectures\">Lecture materials<\/h3>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/lecture01_2021.pdf\">Lecture notes 1<\/a> &#8211; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/pc01_2021.pdf\">Presentation 1<\/a> (Introduction to probability calculus)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/lecture02_2021.pdf\">Lecture notes 2<\/a> &#8211; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/pc02_2021.pdf\">Presentation 2<\/a> (Conditional probability)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/lecture03_2021.pdf\">Lecture notes 3 <\/a>&#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/pc03_2021.pdf\">Presentation 3<\/a> (Independence of events. Bernoulli process)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/lecture04_2021.pdf\">Lecture notes 4<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/pc04_2021.pdf\">Presentation 4 <\/a>(Intro to random variables)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/lecture05_2021.pdf\">Lecture notes 5<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/pc05_2021.pdf\">Presentation 5<\/a> (Cumulative Distribution Function. Intro to Expected Values)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/lecture06_2021.pdf\">Lecture notes 6<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/pc06_2021.pdf\">Presentation 6 <\/a>(Expected values cont.)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/lecture07_2021.pdf\">Lecture notes 7<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/pc07_2021.pdf\">Presentation 7<\/a> (Variance, moments)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/lecture08_2021.pdf\">Lecture notes 8 <\/a>&#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/pc08_2021.pdf\">Presentation 8<\/a> (Intro to random vectors)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/lecture09_2021.pdf\">Lecture notes 9<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/pc09_2021.pdf\">Presentation 9<\/a> (Independence of RV)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/lecture10_2021.pdf\">Lecture notes 10<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/pc10_2021.pdf\">Presentation 10 <\/a>(Conditional Expected Value)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2022\/01\/lecture11_2021.pdf\">Lecture notes 11<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2022\/01\/pc11_2021.pdf\">Presentation 11<\/a> (Chebyshev Inequalities, Convergence of RV, Laws of Large Numbers)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2022\/01\/lecture12_2021.pdf\">Lecture notes 12<\/a> &#8212; <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2022\/01\/pc12_2021.pdf\">Presentation 12<\/a> (Central Limit Theorem)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2022\/02\/pc13_2021.pdf\">Presentation 13<\/a> (Important distributions)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"classes\">Class materials<\/h3>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/problems00_2021.pdf\">Problem set 0<\/a> (6.10.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/problems01_2021.pdf\">Problem set 1<\/a> (13.10.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/problems02_2021.pdf\">Problem set 2<\/a> (20.10.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/problems03_2021.pdf\">Problem set 3<\/a> (27.10.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/problems04_2021.pdf\">Problem set 4<\/a> (3.11.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/problems05_2021.pdf\">Problem set 5<\/a> (10.11.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/problems06_2021.pdf\">Problem set 6<\/a> (17.11.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/problems07_2021.pdf\">Problem set 7<\/a> (24.11.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/problems08_2021.pdf\">Problem set 8<\/a> (1.12.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/problems09_2021.pdf\">Problem set 9 <\/a>(8.12.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/problems10_2021.pdf\">Problem set 10<\/a> (15.12.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/problems11_2021.pdf\">Problem set 11<\/a> (22.12.2021)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2022\/01\/problems12_2021.pdf\">Problem set 12<\/a> (19.01.2022)<\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2022\/01\/problems13_2021.pdf\">Problem set 13<\/a> (26.01.2022)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"homework\">Homework Assignments<\/h3>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/homework1_2021.pdf\">Homework 1<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/homework2_2021.pdf\">Homework 2<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/homework3_2021.pdf\">Homework 3<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/11\/homework4_2021.pdf\">Homework 4<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/12\/homework5_2021.pdf\">Homework 5<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"other\">Course rules<\/h3>\n\n\n\n<p><a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/10\/rules2021.pdf\">Rules<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Old exams<\/h3>\n\n\n\n<p>Midterms: <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2019.pdf\">2020<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2018.pdf\">2019<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2019.pdfhttp:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2017.pdf\">2018<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2016.pdf\">2017<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2015.pdf\">2016<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2014.pdf\">2015<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2013.pdf\">2014<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/midterm_2012.pdf\">2013<\/a>   <\/p>\n\n\n\n<p>1st term: <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final1_2019.pdf\">2020<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final1_2018.pdf\">2019<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final1_2017.pdf\">2018<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final1_2016.pdf\">2017<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final1_2015.pdf\">2016<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final1_2014.pdf\">2015<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final1_2013.pdf\">2014<\/a> <a href=\"http:\/\/2012\">2013<\/a><\/p>\n\n\n\n<p>2nd term: <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2019.pdf\">2020<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2018.pdf\">2019<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2017.pdf\">2018<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2016.pdf\">2017<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2015.pdf\">2016<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2014.pdf\">2015<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2013.pdf\">2014<\/a> <a href=\"http:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-content\/uploads\/sites\/7\/2021\/01\/final2_2012.pdf\">2013<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Winter semester 2021\/2022 Lectures &#8212; Classes &#8212; Homework &#8212; Other Lecture materials Lecture notes 1 &#8211; Presentation 1 (Introduction to probability calculus) Lecture notes 2 &#8211; Presentation 2 (Conditional probability) Lecture notes 3 &#8212; Presentation 3 (Independence of events. Bernoulli process) Lecture notes 4 &#8212; Presentation 4 (Intro to random variables) Lecture notes 5 &#8212;&hellip; <a class=\"more-link\" href=\"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/teaching-materials\/pc\/\">Czytaj dalej <span class=\"screen-reader-text\">Probability Calculus<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":32,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/pages\/558"}],"collection":[{"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/comments?post=558"}],"version-history":[{"count":10,"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/pages\/558\/revisions"}],"predecessor-version":[{"id":771,"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/pages\/558\/revisions\/771"}],"up":[{"embeddable":true,"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/pages\/32"}],"wp:attachment":[{"href":"https:\/\/strony.wne.uw.edu.pl\/ajanicka\/wp-json\/wp\/v2\/media?parent=558"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}