{"id":4190,"date":"2026-01-16T10:07:30","date_gmt":"2026-01-16T10:07:30","guid":{"rendered":"https:\/\/devserver.admin.uoc.gr\/damsl\/?page_id=4190"},"modified":"2026-01-16T12:16:03","modified_gmt":"2026-01-16T12:16:03","slug":"damsl-092-probability-theory","status":"publish","type":"page","link":"https:\/\/mscs.uoc.gr\/damsl\/damsl-092-probability-theory\/","title":{"rendered":"DAMSL-092 Probability Theory"},"content":{"rendered":"\t\t
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\n\t\t\t\t\t\t\t\t\tType<\/strong>
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Preparatory<\/strong>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\t\t\t\tCourse Code<\/strong>
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DAMSL-092<\/strong>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\t\t\t\tTeaching Semester<\/strong>
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A semester<\/strong>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\t\t\t\tECTS Credits<\/strong>
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5<\/strong>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Student Performance Evaluation<\/h6>

Homework Assignments, Final Exam<\/p><\/div><\/div><\/div>

Prerequisite Courses<\/h6>

Calculus I<\/p><\/div><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Syllabus<\/span><\/h6>
  • Introduction to probability: Random experiments,\u00a0probability axioms,\u00a0conditional probability,\u00a0law of total probability, Bayes\u2019 rule, and counting methods.<\/li>
  • Random variables and their distributions: Single and multiple random variables, expectation, variance, moment generating factors, inequalities.<\/li>
  • Limit theorems: Convergence of random variables, weak law of large numbers, central limit theorem.<\/li><\/ul><\/div><\/div><\/div>
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    Learning Outcomes<\/span><\/h6>

    Upon completion of the course the students will have:<\/p>

    • Good knowledge of the basic concepts in probabilities: random experiments and axioms, conditional probability, Bayes law.\u00a0<\/li>
    • Good knowledge of random variables and their distributions, expectation, and variance. Law of large numbers.<\/li><\/ul><\/div><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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      <\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

      Type PreparatoryCourse Code DAMSL-092Teaching Semester A semesterECTS Credits 5 Student Performance Evaluation Homework Assignments, Final Exam Prerequisite Courses Calculus I Syllabus Introduction to probability: Random experiments,\u00a0probability axioms,\u00a0conditional probability,\u00a0law of total probability, Bayes\u2019 rule, and counting methods. Random variables and their distributions: Single and multiple random variables, expectation, variance, moment generating factors, inequalities. Limit theorems: Convergence of random variables, weak law of large numbers, central limit theorem. \u00a0 Learning Outcomes Upon completion of the course the students will have: Good knowledge of the basic concepts in probabilities: random experiments and axioms, conditional probability, Bayes law.\u00a0 Good knowledge of random variables and their distributions, expectation, and variance. Law of large numbers.<\/p>\n","protected":false},"author":194,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-4190","page","type-page","status-publish","hentry","post-no-thumbnail"],"acf":[],"_links":{"self":[{"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/pages\/4190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/users\/194"}],"replies":[{"embeddable":true,"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/comments?post=4190"}],"version-history":[{"count":7,"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/pages\/4190\/revisions"}],"predecessor-version":[{"id":4370,"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/pages\/4190\/revisions\/4370"}],"wp:attachment":[{"href":"https:\/\/mscs.uoc.gr\/damsl\/wp-json\/wp\/v2\/media?parent=4190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}