(Spotlight) Disjoint vs. Independent

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Introduction to Probability and Data

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Duke University

Introduction to Probability and Data

2746 notes

Cours 1 sur 5 dans Specialization Statistics with R

This course introduces you to sampling and exploring data, as well as basic probability theory and Bayes' rule. You will examine various types of sampling methods, and discuss how such methods can impact the scope of inference. A variety of exploratory data analysis techniques will be covered, including numeric summary statistics and basic data visualization. You will be guided through installing and using R and RStudio (free statistical software), and will use this software for lab exercises and a final project. The concepts and techniques in this course will serve as building blocks for the inference and modeling courses in the Specialization.

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Introduction to Probability

<p>Welcome to Week 3 of Introduction to Probability and Data! Last week we explored numerical and categorical data. This week we will discuss probability, conditional probability, the Bayes’ theorem, and provide a light introduction to Bayesian inference. </p><p>Thank you for your enthusiasm and participation, and have a great week! I’m looking forward to working with you on the rest of this course. </p>

Introduction5:49

Disjoint Events + General Addition Rule9:28

Independence9:58

Probability Examples9:02

(Spotlight) Disjoint vs. Independent2:30

Rencontrer les enseignants

Mine Çetinkaya-Rundel
Associate Professor of the Practice
Department of Statistical Science

In this spotlight video, we're going to discuss disjoint and independent events.

These are two terms that sound like each other, and that

are often confused with each other, so we're going to take

a step back again and redefine them, and give some examples

that highlight why they really do not mean the same thing.

As a quick reminder, two events that are disjoint,

also called mutually exclusive, cannot happen at the same time.

While two

processes are independent if knowing the outcome of one

provides no useful information about the outcome of the other.

So disjointness is about events happening at the same time.

So if events A and B are disjoint, probability of A and B is 0.

While independence is about processes not affecting each other.

So if events A and B are independent, probability of A given B is equal to

simply probability of A.

Say we're interested in the eye color of babies.

And the only possibilities are blue, green, and brown.

And yes, there are some people who have one eye blue, and one eye green.

But we're going to ignore that possibility and assume that the

baby can have either blue eyes, green eyes, or brown eyes.

Suppose there's one baby, the possible eye colors are blue, green, and brown.

These outcomes are disjoints, since they

can not happen at the same time.

Now suppose there are two babies, and suppose that

we know that the first one has blue eyes.

The possibilities for the second one are, again, blue, green ,and brown.

These three outcomes for the second baby are also disjoint from each other.

However, the eye color of the first and second baby may

be dependent or independent depending on whether the babies are related or

randomly drawn from the population.

If the babies are related and we know that one has blue eyes,

the other one is going to be more likely to also have blue eyes.

But if not related and they're randomly drawn

from the population, the fact that the first

one has blue eyes will not provide any

useful information about the second one having blue eyes.

One last item to note is that the disjoint outcomes,

the color of one baby's eyes, blue, green,

or brown, are also dependent on each other.

Because if we know that the baby has blue

eyes, we also know that it doesn't have green or

brown eyes We can generalize this to say that disjoint

offense with non-zero probability are always dependent on each other.

Because if we know that one happened, we know that the other one cannot happen.

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