Probability and Statistics

Descriptive Statistics

• Central Tendency: Mean, Median, Mode

• Dispersion: Variance, Standard Deviation, Range

• Quartiles and Percentiles

Probability Theory

• Sample Space ($\Omega$) and Events

• Axioms of Probability

• Conditional Probability: $P(A|B)$

• Independence

• Bayes’ Theorem

Random Variables

• Discrete Distributions

  • PMF and CDF

  • Bernoulli, Binomial, Poisson

• Continuous Distributions

  • PDF and CDF

  • Uniform, Exponential

  • Normal (Gaussian) Distribution

• Expectation $E[X]$ and Variance $Var(X)$ properties

• Central Limit Theorem

Statistical Inference

• Estimation

  • Point Estimators (Bias, Consistency)

• Confidence Intervals

  • For Population Mean (known/unknown $\sigma$)

  • For Population Proportion

• Hypothesis Testing

  • Chi-Square Distribution

  • Student’s t-test

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