Week 1: Introduction. Axiomatic definition and properties of probability.
Week 2: Conditional probability, Bayes' theorem. Independence of events.
Week 3: Random variables. Probability mass function and cumulative distributibution function for discrete random variables.
Week 4: - Expectation, variance, moments, moment generating function, Chebyshev's inequality.
- Standard discrete distributions and their properties: Bernoulli, Binomial
Week 5: - Standard discrete distributions (continued): Geometric, Negative Binomial, Hypergeometric, Poisson.
- Introduction to continuous random variables. Probability density function and cumulative distribution function of continuous random variables.
Week 6: - Expectation, variance moments, percentiles for continuous random variables.
- Standard continuous distributions and properties: Uniform, Exponential, Gamma, Normal.
Week 7: Joint distributions, marginal and conditional distributions, moments, independence of random variables.
Week 8: Covariance, correlation. Central Limit theorem. Descriptive statistics, graphical representation of data
Week 9: - Measures of location and variability.
- Introduction to Point estimation. Unbiased estimators, consistency.
Week 10: - Method of moments. Maximum likelihood estimation.
- Confidence intervals for means and proportions.
Week 11: Testing of hypothesis: Null and Alternate hypothesis, Neyman Pearson lemma.
Week 12: Tests for one sample and two sample problems for normal populations. Tests for proportions. Large sample tests.
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