Probability theory,inequality
This course introduces important concepts in probability theory using clear definitions, properties, and theorems .
• Generating Functions – Definition of probability generating functions and moment generating functions, their properties, and how they are used to find mean, variance, and higher moments.
• Cumulants – Definition of cumulants, relation between moments and cumulants, and basic properties.
• Characteristic Functions – Simple definition, basic properties, and main theorems on uniqueness and convergence .
• Chebyshev’s Inequality – Statement and proof of the inequality, with applications in bounding probabilities.
• Weak Law of Large Numbers (WLLN) – Statement and proof of the theorem, showing that the sample average approaches the expected value in probability.
The course aims to give students a clear understanding of these tools at the level of definitions, properties, and main results, which are essential for further study in probability and statistics.
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Mrs. S. Mahalakshmi, M.Sc., M.Phil., B.Ed., SET Assistant Professor of Statistics (Specialization in Mathematics). I am working as an Assistant Professor of Statistics with an academic background in Mathematics. I hold M.Sc. and M.Phil. degrees in Mathematics, a B.Ed., and have qualified the State Eligibility Test (SET). My teaching interests include Probability Theory, Operations Research, Statistical Methods, Algebra, Real Analysis, and Complex Analysis. I am passionate about guiding students, connecting mathematical theory with statistical applications, and encouraging them to build strong analytical and problem-solving skills.
