1. Making use of multivariate distributions
Welcome to this course on advanced probability and distributions!
2. The role of probability and distributions in business decisions
Probability and distributions underpin a lot of concepts and techniques for business analysis and data-driven decision making. It allows us to quantify uncertainty, assess risks, and ultimately make better data-driven choices.
3. Course overview
This course is divided into three chapters:
In Chapter 1, we begin by exploring probability distributions, including multivariate distributions, to understand relationships between multiple business variables.
Next, we'll focus on techniques like confidence intervals and expected value calculations that help businesses assess and mitigate uncertainty.
Finally, we introduce powerful simulation methods such as Monte Carlo simulations and decision trees to model and optimize business strategies.
By the end of this course, you'll be equipped with probability-based tools to analyze data, manage uncertainty, and make more strategic decisions.
4. Prerequisite knowledge and skills
Before diving into advanced techniques for better business decisions, let's review what you should know first.
This course builds on key statistical concepts, so we recommend completing the “Introduction to Statistics” course on DataCamp first, if you haven't already.
In this lesson, we'll explore how multivariate distributions help analyze multiple business variables, starting with a quick refresher on univariate distributions.
5. Univariate distributions
A univariate distribution describes the probabilities associated with a single variable. It tells us how likely different values of a single metric are to occur. For example, average daily temperature.
Understanding such a distribution helps summarize data and make informed decisions. However, real-world data is often more complex and involves multiple factors simultaneously, which is where multivariate distributions come into play.
6. Multivariate distributions
Multivariate distributions help us analyze two or more variables interacting with each other and changing together.
For example, taking into account both the temperature and whether or not it snows.
By studying these patterns, we can uncover insights that wouldn't be visible when looking at each variable separately.
7. Joint probability
Specifically, multivariate distributions allow us to explore joint probability, the likelihood of different variables taking on specific values at the same time.
Joint probability tells us the chance of multiple things happening at the same time, like it raining and people buying umbrellas.
8. Example: coffee shop
Imagine you own a coffee shop and want to understand customer behavior. Two key factors you're tracking are: how much customers spend and how long they stay in the shop.
If you were to analyze these two factors separately, you might find things like: most customers spend around $5, or
most customers stay for about 30 minutes.
However, what if these two factors are related? Do customers who stay longer tend to spend more? A multivariate distribution and joint probability help us see patterns in how two or more factors interact.
9. Example: coffee shop
For example, you might find that customers who stay for more than an hour tend to spend 30% more on average than those who stay less than 30 minutes. This insight could help you decide to offer discounts on second purchases or encourage longer visits with comfortable seating.
10. Let's practice!
Time to practice!