PY CGL SI 2025
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UNIT I Probability, Random Variables & Distribution Theory
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Probability Theory Introduction Class
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Probability Problems & Solutions
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Probability - Addition Theorem
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Total Probability and Bayes Theorem
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Random Variables Introduction and CDF - Discrete Random Variables
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Continuous Random Varaibles, Mean and Variance
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Bivariate random Variables, Marginal and conditional distributions
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Mathematical Expectation and Conditional Expectation
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Conditional probability Problems
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Convergence in Probability & Weak and Strong laws of large numbers
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MGF, Cumulant Generating Functions and Characteristic Function
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Characteristic Functions Properties and Problems
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Lindberg-Levy and Lyapunov’s Theorem
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Binomial Distribution
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Poisson and Hypergeometric Distribution
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Uniform and Normal Distribution
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Gamma and Exponential Distributions
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Beta distribution of first and second kind
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UNIT VII Differential Equations and Operations Research
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Differential Equations - Introduction Class
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Linear ODE With Constant Coefficients Complementary Function
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Linear ODE with Constant coefficients - Finding Particular Integral Type I and II
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Linear ODE with Constant Coefficients Finding Particular Integral Type III and IV
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Liner Higher Order ODE with Variable Coefficients Introduction Class
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Method of Variation of Parameters, Linearly Dependent and Linearly Independent
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Wronskian Properties and Problems with Solutions
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Second Order ODE with Ordinary and Singular Points
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Indicial Equations and Introduction of Bessels Equations
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Bessels Equations of first and second kind
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Bessels Functions, Recurrence Formula and Problems
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