This chapter introduces you to probability concepts that help uncover interactions between variables. By exploring multivariate distributions, conditional probability, and Markov Chains, you will gain insights into how probability-driven models can predict customer behavior, optimize strategies, and assess risks. These tools provide a solid foundation for making data-driven business decisions in uncertainty.

Making use of multivariate distributions

Usefulness of multivariate distributions

Matching business questions

Interpreting joint probability

Applying conditional probability

Using Bayes' Theorem for decision-making

Practicing conditional probability concepts

Interpreting conditional probability

Markov Chain analysis

Using Markov Chain analysis

Visualizing a Markov Chain

Interpreting a Markov Chain analysis

Advanced Probability for Business Decisions

Chapter 2 focuses on interpreting and managing uncertainty with respect to business outcomes. Learners will learn about common techniques like expected value calculations, confidence and prediction intervals, scenario analysis and sensitivity analysis. 

Expected value calculations

Determining probabilities

Expected value calculation steps

Choosing between stock options

Interpreting confidence and prediction intervals

Meaning of the confidence interval

Confidence vs. prediction intervals

Choosing the right laptop

Scenario analysis

Considering scenarios

Steps of scenario analysis

Recommending action based on scenario analysis

Sensitivity analysis

Scenario analysis vs. sensitivity analysis

Analyzing and communicating uncertainty

Interpreting a tornado diagram

Interpreting and managing uncertainty

In the final chapter, you will explore how simulation techniques can enhance decision-making in the presence of uncertainty. You will learn to apply resampling methods, Monte Carlo simulations, and decision trees to estimate uncertainty, assess risks, and visualize strategic choices. By integrating these techniques, you will develop the ability to synthesize insights and make data-driven recommendations in business scenarios.

Resampling for limited data

Resampling techniques

Purpose of resampling

The resampling trade-off

Monte Carlo simulation

Ensuring meaningful Monte Carlo simulation results

Options

Key features

Non-applicable features

Key features of Monte Carlo simulation

Interpreting Monte Caro simulation results

Visualizing paths with decision trees

Decision tree building blocks

Decision trees

Decision trees vs. scenario analysis

Interpreting a decision tree

Integrating insights in the decision process

Applying the decision process

Expected value calculation

Choosing the right method

Wrap-up

Simulation Techniques for Decision Support

Uncertainty is a constant in business, but you don’t have to rely on guesswork to make decisions. This course will equip you with advanced statistical and simulation techniques to model uncertainty, assess risk, and make data-driven strategic choices. Through hands-on exercises, you’ll learn how to apply probability concepts, scenario planning, Monte Carlo simulations, and decision trees to real-world business challenges.

You’ll start by building a strong foundation in probability, exploring multivariate distributions, conditional probability, and Markov Chains to uncover patterns in business data. Next, you’ll dive into measuring and managing uncertainty using expected value analysis, confidence intervals, and sensitivity testing. Finally, you’ll apply simulation techniques like resampling, Monte Carlo methods, and decision trees to evaluate complex scenarios and turn insights into actionable strategies.

By the end of this course, you’ll have the skills and confidence to apply data-driven techniques in your decision-making process—helping you navigate uncertainty, mitigate risks, and drive better business outcomes.

<h2>Understanding Probability and Uncertainty in Business</h2>
Uncertainty is an inherent part of decision-making, but advanced probability techniques allow us to model and manage it effectively. This course begins with a deep dive into probability fundamentals, focusing on multivariate distributions, conditional probability, and Markov Chains. You will learn how to analyze data dependencies, assess likelihoods, and quantify uncertainty in business environments. By mastering these core principles, you will develop a structured approach to making informed decisions under uncertain conditions.

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<h2>Quantifying and Measuring Risk</h2>
Once the foundational concepts are in place, you will explore techniques to quantify and mitigate risk. Through expected value analysis, confidence intervals, scenario analysis, and sensitivity testing, you will learn how to measure the impact of uncertainty on business outcomes. These methods will enable you to assess potential risks in investment decisions, operational strategies, and market forecasts. With hands-on exercises, you will gain practical experience in applying probability-driven insights to real-world data, ensuring that your strategic choices are backed by statistical rigor.

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<h2>Advanced Simulation and Decision-Making Techniques</h2>
The final section of this course focuses on powerful simulation techniques used to navigate complex decision-making scenarios. You will explore Monte Carlo simulations, resampling methods, and decision trees to evaluate multiple potential outcomes and optimize strategic planning. These tools will help you model uncertainty, simulate different business scenarios, and make data-driven recommendations with confidence. By the end of the course, you will be equipped with the skills to leverage probability and simulation techniques in high-stakes business environments, driving more precise and strategic decision-making.

Introduction to Statistics

Develop a better intuition for advanced probability, risk assessment, and simulation techniques to make data-driven business decisions with confidence.

Advanced Probability: Uncertainty in Data

Analyze how users go from free trail to a paid subscription or cancellation to predict long-term retention.

Model how streaming prices evolve over time based on historical patterns of movement between different price ranges. 

Estimate profitability of a seasonal discount strategy by computing expected profits under different sales conditions.

Assessing a new subscription tier by anticipating the number of subscribed users based on past adoption rates. 

Assess potential revenue outcomes for a new product by testing thousands of different demand and cost conditions.

Choosing the right method

Advanced Probability: Uncertainty in Data

Exercício interativo prático