Statistics And Probability

"Statistics and probability involve data analysis, trends, predictions, sampling, distributions, randomness, variance, mean, correlation, hypothesis testing, outcomes.

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Language : English
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Description Course Content How To Use

Description:

Statistics and probability are branches of mathematics that deal with data analysis, uncertainty, and prediction. Statistics involves collecting, analyzing, interpreting, and presenting data. Probability focuses on the likelihood of events occurring. Together, they are used to make informed decisions, model random processes, and understand patterns in real-world phenomena.

Key Highlights:

Data Analysis: Statistics helps collect, organize, and interpret data to identify trends and patterns.
Probability: Measures the likelihood of events occurring, ranging from 0 (impossible) to 1 (certain).
Distributions: Describes how data points are spread (e.g., normal, binomial distributions).
Sampling: Involves selecting a subset of data to make inferences about a larger population.
Hypothesis Testing: Assesses the validity of assumptions using statistical methods and significance levels.

What you will learn:

Data Summarization: Learn how to calculate measures like mean, median, mode, and standard deviation.
Probability Rules: Understand how to calculate the likelihood of events using basic probability principles.
Distributions: Learn about different data distributions (e.g., normal, binomial) and their properties.
Statistical Inference: Master methods like hypothesis testing and confidence intervals to draw conclusions from data.
Correlation and Regression:Understand relationships between variables and how to model them mathematically.

Module 1: Introduction to Statistics and Probability

Topic
Session-1: Descriptive Statistics
Types of Data: Qualitative vs. Quantitative
Measures of Central Tendency (Mean, Median, Mode)
Measures of Dispersion (Variance, Standard Deviation, Range, Interquartile Range)
Shape of Distribution: Skewness, Kurtosis
Visualizations: Histogram, Boxplot, Bar chart
Session-2: Introduction to Probability
Basics of Probability
Probability Rules (Addition and Multiplication Rules)
Conditional Probability and Bayes’ Theorem
Independence vs. Dependence
Session-3: Combinatorics
Permutations and Combinations
Applications in Probability

Module 2: Probability Distributions

Topic
Session-4: Discrete Probability Distributions
Bernoulli Distribution
Poisson Distribution
Session-5: Continuous Probability Distributions
Uniform Distribution
Exponential Distribution
Session-6: Sampling Distributions
Law of Large Numbers
Central Limit Theorem
Understanding the Concept of Sampling Distribution of a Statistic (Mean, Proportion)

Module 3: Inferential Statistics

Topic
Session-7: Point Estimation and Confidence Intervals
Estimating Population Parameters
Confidence Intervals for Means and Proportions
Session-8: Hypothesis Testing
Null and Alternative Hypotheses
Type I and Type II Errors
p-Values and Significance Level (α)
Z-test, T-test (1-sample, 2-sample, Paired t-tests)
Chi-Square Test for Independence
ANOVA (Analysis of Variance)
Session-9: Non-Parametric Tests
Wilcoxon Rank-Sum Test
Kruskal-Wallis Test
Mann-Whitney U Test

Module 4: Advanced Probability and Statistics

Topic
Session-10: Bayesian Statistics
Introduction to Bayesian Thinking
Bayesian Inference
Prior, Likelihood, Posterior
Session-11: Markov Chains
Introduction to Markov Processes
Transition Matrix and State Probability
Applications in Time Series and Random Processes
Session-12: Multivariate Statistics
Covariance and Correlation Matrix
Principal Component Analysis (PCA)
Factor Analysis

Module 5: Regression and Predictive Modeling

Session-13: Simple Linear Regression
Line of Best Fit
Coefficients and Interpretation
Residual Analysis and Assumptions of Regression
Session-14: Multiple Linear Regression
Multiple Predictors
Variance Inflation Factor (VIF) and Multicollinearity
Model Evaluation: R-squared, Adjusted R-squared, AIC/BIC
Session-15: Logistic Regression
Odds Ratio and Log Odds
Maximum Likelihood Estimation (MLE)
ROC Curve, AUC, Precision-Recall

Module 6: Time Series Analysis

Topic
Session-16: Introduction to Time Series Data
Components of Time Series: Trend, Seasonality, Noise
Stationarity and Differencing
Session-17: Time Series Forecasting Models
Moving Averages and Exponential Smoothing
ARIMA (AutoRegressive Integrated Moving Average)
Seasonal Decomposition of Time Series (STL)
Time Series in Python
Plotting and Decomposing Time Series Data
Building ARIMA Models and Forecasting

Module 7: Applied Probability in Machine Learning

Topic
Session-18: Decision Trees and Random Forests
Gini Index and Entropy
Understanding Feature Importance
Session-19: Naive Bayes Classifier
Theoretical Foundation
Multinomial, Gaussian, and Bernoulli Naive Bayes
Session-20: Probabilistic Graphical Models
Introduction to Bayesian Networks
Inference and Prediction using PGMs

Module 8: Data Testing & Quality Assurance with Statistics

Topic
Session-21: AB Testing
Experimental Design
Hypothesis Testing for Business Decisions
Session-22: Data Validation Techniques
Detecting Anomalies in Data
Statistical Quality Control
Application of Control Charts
Session-23: Statistical Modeling for ETL Processes
Outlier Detection
Data Profiling using Statistical Methods

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