MATS 2105 Mathematical Probability I Exam 2023

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MATS 2105: First Semester Examination, University of Bamenda, Faculty of Science, Department of Maths and Computer Science, Lecturer Bime Markdonal, 02-02-2023, Hall PBB08: a comprehensive 43-part foundations exam spanning probability theory (sample spaces, sigma-algebras, events, probability axioms, conditional probability, the law of total probability, independence, random variables, expectation/variance, the Binomial distribution via a coin-toss experiment), propositional/predicate logic (implications, tautologies, negation of quantified statements), set theory and functions (Cartesian products, injections/surjections, preimages, relations and their composition/complement), elementary number theory (induction proofs, gcd/lcm, Bezout's identity, modular exponentiation), and abstract algebra (cyclic groups, permutations and cycle decomposition, group homomorphisms/isomorphisms/kernels, cosets and Lagrange's theorem, subgroup correspondence, ring homomorphisms, ideals, subrings, PIDs, and maximal/prime ideals).