Study probability theory and statistical analysis
322
Sub Topics
708
MCQs
344
MCOs
516
True/False
291
Fill Blanks
94
Rearrange
285
Matching
143
Comprehensions
271
Flashcard Decks
Curriculum
What You'll Learn
01 Introduction to Probability and Statistics 4 topics
1 Basic Concepts and Terminology
- Definitions of Probability and Statistics
- Applications and Importance
- Historical Development
2 Types of Data
- Qualitative vs. Quantitative
- Discrete vs. Continuous
- Nominal, Ordinal, Interval, and Ratio Scales
3 Data Collection Methods
- Sampling Techniques
- Experimental Design
- Observational Studies
4 Data Representation
- Tables and Charts
- Graphical Methods
- Frequency Distributions
02 Descriptive Statistics 5 topics
1 Measures of Central Tendency
- Mean
- Median
- Mode
- Weighted Averages
2 Measures of Dispersion
- Range
- Variance
- Standard Deviation
- Coefficient of Variation
- Interquartile Range
3 Measures of Position
- Percentiles
- Quartiles
- Standardized Scores (z-scores)
4 Measures of Shape
- Skewness
- Kurtosis
5 Exploratory Data Analysis
- Box Plots
- Stem-and-Leaf Displays
- Scatter Plots
03 Probability Theory 4 topics
1 Basic Probability Concepts
- Sample Space and Events
- Axioms of Probability
- Properties of Probability
2 Counting Techniques
- Multiplication Principle
- Permutations
- Combinations
3 Conditional Probability
- Definition and Properties
- Independence of Events
- Law of Total Probability
4 Bayes' Theorem
- Prior and Posterior Probabilities
- Applications of Bayes' Theorem
- Bayesian Inference
04 Discrete Random Variables and Probability Distributions 3 topics
1 Random Variables
- Definition and Types
- Probability Mass Function (PMF)
- Cumulative Distribution Function (CDF)
2 Expected Value and Variance
- Mean of a Discrete Random Variable
- Variance and Standard Deviation
- Properties of Expectation and Variance
3 Common Discrete Distributions
- Bernoulli Distribution
- Binomial Distribution
- Geometric Distribution
- Negative Binomial Distribution
- Hypergeometric Distribution
- Poisson Distribution
05 Continuous Random Variables and Probability Distributions 3 topics
1 Continuous Random Variables
- Probability Density Function (PDF)
- Cumulative Distribution Function (CDF)
- Properties of Continuous Distributions
2 Expected Value and Variance
- Mean of a Continuous Random Variable
- Variance and Standard Deviation
- Moments of Continuous Distributions
3 Common Continuous Distributions
- Uniform Distribution
- Normal (Gaussian) Distribution
- Exponential Distribution
- Gamma Distribution
- Beta Distribution
- Chi-Square Distribution
- Student's t-Distribution
- F-Distribution
- Weibull Distribution
- Lognormal Distribution
06 Multivariate Distributions 5 topics
1 Joint Probability Distributions
- Joint PMF and PDF
- Joint CDF
- Marginal Distributions
2 Conditional Distributions
- Conditional PMF and PDF
- Conditional Expectation
3 Independence of Random Variables
- Definition and Properties
- Testing for Independence
4 Covariance and Correlation
- Definition and Properties
- Correlation Coefficient
- Rank Correlation
5 Multivariate Normal Distribution
- Properties and Parameters
- Applications
07 Functions of Random Variables 3 topics
1 Transformations of Random Variables
- Linear Transformations
- Non-linear Transformations
2 Distribution of Functions of Random Variables
- Method of Transformations
- Moment Generating Functions
- Characteristic Functions
3 Order Statistics
- Distributions of Order Statistics
- Sample Minimum and Maximum
- Sample Median
08 Sampling Distributions 6 topics
1 Sampling Theory
- Population vs. Sample
- Statistics and Sampling Distributions
- Standard Error
2 Sampling Distribution of the Mean
- Expected Value and Variance
- Central Limit Theorem
- Applications and Examples
3 Sampling Distribution of Variance
- Chi-Square Distribution
- Properties and Applications
4 Sampling Distribution of Proportions
- Normal Approximation
- Properties and Applications
5 Student's t-Distribution
- Properties and Applications
- Relationship with Normal Distribution
6 F-Distribution
- Properties and Applications
- Ratio of Variances
09 Estimation Theory 4 topics
1 Point Estimation
- Properties of Estimators
- Methods of Finding Estimators
- Maximum Likelihood Estimation
- Method of Moments
2 Interval Estimation
- Confidence Intervals for Means
- Confidence Intervals for Proportions
- Confidence Intervals for Variances
- Confidence Intervals for Differences
3 Sample Size Determination
- For Estimating Means
- For Estimating Proportions
- Precision and Confidence Level
4 Bayesian Estimation
- Prior and Posterior Distributions
- Bayesian Point Estimates
- Credible Intervals
10 Hypothesis Testing 7 topics
1 Fundamentals of Hypothesis Testing
- Null and Alternative Hypotheses
- Type I and Type II Errors
- Power of a Test
- p-values and Significance Levels
2 Tests for a Single Mean
- z-Test
- t-Test
- One-tailed vs. Two-tailed Tests
3 Tests for a Single Proportion
- z-Test for Proportions
- Exact Tests
4 Tests for a Single Variance
- Chi-Square Test
- Applications
5 Tests for Comparing Two Populations
- Independent vs. Paired Samples
- Tests for Two Means
- Tests for Two Proportions
- Tests for Two Variances
6 Tests for Multiple Populations
- Analysis of Variance (ANOVA)
- Multiple Comparison Procedures
7 Nonparametric Tests
- Sign Test
- Wilcoxon Signed-Rank Test
- Mann-Whitney U Test
- Kruskal-Wallis Test
- Runs Test
11 Correlation and Regression 7 topics
1 Correlation Analysis
- Pearson's Correlation Coefficient
- Testing for Significant Correlation
- Spearman's Rank Correlation
2 Simple Linear Regression
- Model Specification
- Method of Least Squares
- Properties of Regression Estimators
- Coefficient of Determination
3 Inference in Regression Analysis
- Standard Errors of Regression Coefficients
- Confidence Intervals
- Hypothesis Testing
- ANOVA in Regression
4 Prediction and Forecasting
- Point Prediction
- Prediction Intervals
- Forecasting Methodology
5 Regression Diagnostics
- Residual Analysis
- Detecting Outliers and Influential Points
- Testing Model Assumptions
6 Multiple Regression
- Model Specification
- Estimation and Inference
- Partial Correlation
- Multicollinearity
- Variable Selection Methods
7 Nonlinear Regression
- Transformations to Linearity
- Polynomial Regression
- Logistic Regression
12 Analysis of Categorical Data 4 topics
1 Contingency Tables
- One-Way Tables
- Two-Way Tables
- Multi-Way Tables
2 Chi-Square Tests
- Goodness-of-Fit Test
- Test of Independence
- Test of Homogeneity
3 Measures of Association
- Phi Coefficient
- Contingency Coefficient
- Cramer's V
- Lambda
- Odds Ratio and Relative Risk
4 Logistic Regression
- Binary Logistic Regression
- Multinomial Logistic Regression
- Ordinal Logistic Regression
13 Experimental Design and Analysis of Variance 6 topics
1 Principles of Experimental Design
- Randomization
- Replication
- Blocking
- Factorial Designs
2 One-Way ANOVA
- Model and Assumptions
- The F-Test
- Multiple Comparisons
3 Two-Way ANOVA
- Main Effects and Interactions
- With Replication
- Without Replication
4 Multi-Factor ANOVA
- Model Specification
- Analysis and Interpretation
5 Repeated Measures Designs
- One-Factor Repeated Measures
- Multi-Factor Designs with Repeated Measures
6 Analysis of Covariance (ANCOVA)
- Model and Assumptions
- Applications and Interpretation
14 Time Series Analysis 5 topics
1 Components of Time Series
- Trend
- Seasonal Variation
- Cyclical Variation
- Irregular Variation
2 Smoothing Techniques
- Moving Averages
- Exponential Smoothing
- Seasonal Adjustment
3 Time Series Regression
- Trend Analysis
- Autocorrelation
- Serial Correlation
4 ARIMA Models
- Autoregressive (AR) Processes
- Moving Average (MA) Processes
- Mixed ARMA Processes
- Integrated Processes
- Box-Jenkins Methodology
5 Forecasting
- Forecasting with ARIMA Models
- Evaluation of Forecasts
- Confidence Intervals for Forecasts
15 Nonparametric Statistics 6 topics
1 Introduction to Nonparametric Methods
- Advantages and Limitations
- Efficiency of Nonparametric Tests
2 Tests for One Sample
- Sign Test
- Wilcoxon Signed-Rank Test
- Kolmogorov-Smirnov Test
3 Tests for Two Independent Samples
- Mann-Whitney U Test
- Kolmogorov-Smirnov Two-Sample Test
- Wald-Wolfowitz Runs Test
4 Tests for Two Related Samples
- Sign Test for Paired Data
- Wilcoxon Signed-Rank Test for Paired Data
- McNemar Test
5 Tests for Multiple Samples
- Kruskal-Wallis Test
- Friedman Test
- Nonparametric Multiple Comparisons
6 Measures of Association
- Spearman's Rank Correlation
- Kendall's Tau
- Goodman and Kruskal's Gamma
16 Introduction to Bayesian Statistics 5 topics
1 Bayesian Philosophy
- Subjective Probability
- Bayesian vs. Frequentist Approaches
2 Prior Distributions
- Informative Priors
- Noninformative Priors
- Conjugate Priors
3 Posterior Analysis
- Posterior Distribution
- Point Estimation
- Interval Estimation
- Predictive Distributions
4 Bayesian Computation
- Markov Chain Monte Carlo (MCMC)
- Gibbs Sampling
- Metropolis-Hastings Algorithm
5 Bayesian Inference
- Hypothesis Testing
- Model Selection
- Bayesian Regression
17 Statistical Quality Control 5 topics
1 Introduction to Quality Control
- Quality Concepts
- Statistical Process Control
2 Control Charts for Variables
- X-bar and R Charts
- X-bar and S Charts
- Individual and Moving Range Charts
3 Control Charts for Attributes
- p Charts
- np Charts
- c Charts
- u Charts
4 Process Capability Analysis
- Capability Indices
- Tolerance Limits
- Performance Measures
5 Acceptance Sampling
- Single Sampling Plans
- Double Sampling Plans
- Multiple Sampling Plans
- Operating Characteristic Curves
18 Multivariate Analysis 7 topics
1 Multivariate Distributions
- Multivariate Normal Distribution
- Wishart Distribution
- Hotelling's T-Square Distribution
2 Principal Component Analysis
- Eigenvalues and Eigenvectors
- Principal Components
- Interpretation and Applications
3 Factor Analysis
- Factor Model
- Factor Extraction
- Factor Rotation
- Factor Scores
4 Discriminant Analysis
- Linear Discriminant Functions
- Classification Procedures
- Evaluation of Discriminant Analysis
5 Cluster Analysis
- Similarity and Distance Measures
- Hierarchical Clustering
- Non-hierarchical Clustering
- Interpretation of Clusters
6 Multidimensional Scaling
- Metric Scaling
- Nonmetric Scaling
- Interpretation and Applications
7 Canonical Correlation Analysis
- Canonical Variables
- Interpretation and Applications
19 Introduction to Machine Learning Statistics 6 topics
1 Statistical Learning Theory
- Supervised vs. Unsupervised Learning
- Bias-Variance Tradeoff
- Overfitting and Regularization
2 Classification Methods
- Logistic Regression
- Discriminant Analysis
- K-Nearest Neighbors
- Support Vector Machines
- Decision Trees and Random Forests
3 Regression Methods
- Ridge Regression
- Lasso Regression
- Elastic Net
- Regression Trees
4 Clustering Methods
- K-Means Clustering
- Hierarchical Clustering
- Density-Based Clustering
5 Dimensionality Reduction
- Principal Component Analysis
- Factor Analysis
- t-SNE
6 Model Evaluation and Selection
- Cross-Validation
- Bootstrap Methods
- Performance Metrics
- Model Selection Criteria
20 Advanced Topics in Statistics 5 topics
1 Survival Analysis
- Censoring and Truncation
- Survival and Hazard Functions
- Kaplan-Meier Estimation
- Log-Rank Test
- Cox Proportional Hazards Model
2 Spatial Statistics
- Spatial Point Processes
- Geostatistics
- Spatial Regression Models
3 Bootstrap Methods
- Nonparametric Bootstrap
- Parametric Bootstrap
- Bootstrap Confidence Intervals
4 Statistical Computing
- Numerical Optimization
- Monte Carlo Methods
- Statistical Software and Programming
5 Stochastic Processes
- Markov Chains
- Poisson Processes
- Brownian Motion
- Queueing Theory
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Probability and Statistics
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