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“Jana Prosason” (Public Administration)( “জনপ্রশাসন”) is authored by Prangovinda Das.(NCBA)
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1. Fundamental Concepts of Probability
- Set Theory and Sample Space: Elements, trials, events, and sample space construction.
- Definitions of Probability: Classical, empirical (statistical), and modern axiomatic definitions of probability.
- Probability Theorems: Addition law of probability, total probability theorem, and basic inequalities.
2. Conditional Probability and Independence
- Conditional Probability: Definition, properties, and sequential experiments.
- Compound Probability: Product/multiplication rule for dependent and independent events.
- Bayes’ Theorem: Prior and posterior probabilities with structural real-world application problems.
3. Random Variables and Distribution Functions
- Discrete and Continuous Random Variables: Probability Mass Function (PMF), Probability Density Function (PDF), and Cumulative Distribution Function (CDF).
- Joint and Marginal Distributions: Bivariate random variables, marginal distributions, conditional distributions, and statistical independence.
4. Mathematical Expectation and Moments
- Expectation and Variance: Expectations of functions of random variables, properties of variance, and covariance.
- Generating Functions: Moment Generating Functions (MGF), Characteristic Functions, and Probability Generating Functions.
5. Probability Distributions
- Discrete Distributions: Uniform, Bernoulli, Binomial, Poisson, Geometric, and Negative Binomial distributions.
- Continuous Distributions: Uniform, Exponential, Gamma, Beta, and Normal (Gaussian) distributions, including their properties and limiting behaviors.
6. Limit Theorems
- Laws of Large Numbers: Weak Law of Large Numbers (WLLN) and Strong Law of Large Numbers (SLLN).
- Central Limit Theorem: De Moivre-Laplace limit theorem and Lindeberg-Lévy Central Limit Theorem.
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