College Final ExamUniversityMathematics

Probability & Statistics (Applied) Study Guide

An applied probability and statistics course for STEM and business students: probability foundations (axioms, counting rules, conditional probability, Bayes' theorem), discrete and continuous distributions, sampling distributions, point and interval estimation, hypothesis testing, ANOVA, regression and correlation, nonparametric methods, and applications in real-world decision-making.

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12 Topics Covered

1

Probability Foundations and Conditional Probability

Sample spaces, axioms, conditional probability, Bayes' theorem, and independence—essential foundations for all subsequent probability calculations.

2

Counting Methods and Combinatorics

Permutations, combinations, and multinomial coefficients for computing probabilities in discrete sample spaces and arrangement problems.

3

Discrete Probability Distributions

Binomial, geometric, Poisson, and hypergeometric distributions with PMFs, expected values, and real-world modeling applications.

4

Continuous Probability Distributions

Normal, exponential, gamma, and related distributions with PDFs, CDFs, and probability calculations using standardization.

5

Joint Distributions and Random Variable Operations

Joint and marginal distributions, covariance, correlation, moment generating functions, and linear combinations of random variables.

6

Sampling Distributions and Central Limit Theorem

Distribution of sample statistics, CLT applications, t-distribution, and chi-squared distribution for statistical inference.

7

Point and Interval Estimation

Unbiased estimators, maximum likelihood, confidence intervals for means, proportions, and variances with proper interpretation.

8

Hypothesis Testing Foundations

Null and alternative hypotheses, Type I/II errors, p-values, power analysis, and effect size interpretation.

9

Inference for Means and Proportions

One-sample, two-sample, and paired t-tests; z-tests for proportions; assumptions verification and test selection.

10

Analysis of Variance (ANOVA)

One-way and two-way ANOVA, F-statistics, interaction effects, post-hoc comparisons, and assumption checking procedures.

11

Regression and Correlation Analysis

Least squares estimation, inference for slope, R-squared interpretation, residual analysis, and multiple regression introduction.

12

Nonparametric Methods and Applied Techniques

Chi-squared tests, Wilcoxon tests, bootstrap methods, Bayesian basics, and quality control applications for robust analysis.

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