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Curriculum
- 8 Sections
- 69 Lessons
- 4 Weeks
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- Before You StartIntroduction4
- Module 1: Introduction to Data Science12
- 3.1Principles of Data Science – Data Analytic Thinking
- 3.2Principles of Data Science – The Data Science Process
- 3.3Further Reading
- 3.4Data Science Technologies – Introduction to Data Science Technologies
- 3.5Data Science Technologies – An Overview of Data Science Technologies
- 3.6Data Science Technologies – Azure Machine Learning Learning Studio
- 3.7Data Science Technologies – Using Code in Azure ML
- 3.8Data Science Technologies – Jupyter Notebooks
- 3.9Data Science Technologies – Creating a Machine Learning Model
- 3.10Data Science Technologies – Further Reading
- 3.11Lab Instructions
- 3.12Lab Verification
- Module 2: Probability & Statistics for Data Science21
- 4.1Probability and Random Variables – Overview of Probability and Random Variables
- 4.2Probability and Random Variables – Introduction to Probability
- 4.3Probability and Random Variables – Discrete Random Variables
- 4.4Probability and Random Variables – Discrete Probability Distributions
- 4.5Probability and Random Variables – Binomial Distribution Examples
- 4.6Probability and Random Variables – Poisson Distributions
- 4.7Probability and Random Variables – Continuous Probability Distributions
- 4.8Probability and Random Variables – Cumulative Distribution Functions
- 4.9Probability and Random Variables – Central Limit Theorem
- 4.10Probability & Random Variables – Further Reading
- 4.11Introduction to Statistics – Overview of Statistics
- 4.12Introduction to Statistics – Descriptive Statistics
- 4.13Introduction to Statistics – Summary Statistics
- 4.14Introduction to Statistics – Demo: Viewing Summary Statistics
- 4.15Introduction to Statistics – Z-Scores
- 4.16Introduction to Statistics – Correlation
- 4.17Introduction to Statistics – Demo: Viewing Correlation
- 4.18Introduction to Statistics – Simpson’s Paradox
- 4.19Introduction to Statistics – Further Reading
- 4.20Introduction to Statistics – Lab Instructions
- 4.21Introduction to Statistics – Lab Verification
- Module 3: Simulation & Hypothesis Testing16
- 5.1Simulation – Introduction to Simulation
- 5.2Simulation – Start
- 5.3Lab
- 5.4Simulation – Demo: Performing a Simulation
- 5.5Simulation – Further Reading
- 5.6Hypothesis Testing – Overview
- 5.7Hypothesis Testing – Introduction
- 5.8Hypothesis Testing – Z-Tests, T-Tests, and Other Tests
- 5.9Hypothesis Testing – Test Examples
- 5.10Hypothesis Testing – Type 1 and Type 2 Errors
- 5.11Hypothesis Testing – Confidence Intervals
- 5.12Hypothesis Testing – Demo with R & Python
- 5.13Hypothesis Testing – Misconceptions
- 5.14Hypothesis Testing – Further Reading
- 5.15Hypothesis Testing – Lab Instructions
- 5.16Hypothesis Testing – Lab Verification
- Module 4: Exploring & Visualizing Data4
- Module 5: Data Cleansing & Manipulation4
- Module 6: Introduction to Machine Learning4
- Final Exam & Survey4
Probability and Random Variables – Poisson Distributions
Poisson Distributions
Downloads and transcripts
Video Transcript
- Start of transcript. Skip to the end.
- Let’s talk about the Poisson distribution.
- The Poisson distribution is a limiting version
- of the Binomial distribution.
- When the number of trials gets really large but
- the probability of success gets smaller at the same rate
- that np essentially becomes this value lambda.
- So you’re no longer gonna have an n and p in the formula for
- the pmf, you’re just gonna have that lambda in there.
- So we would write the X as a Poisson random variable,
- with parameter lambda,
- and then the formula for the PMF looks like this.
- So as long as I know lambda, I have the PMF and
- then I can compute probabilities.
- I’m going to tell you some useful facts about the Poisson
- distribution, namely that its mean is exactly lambda.
- And its variance is also exactly lambda,
- which I think is really cool because it helps me remember it.
- Now whenever I think of the Poisson distribution I think of,
- I’ll be honest, I think of getting kicked by a horse.
- Because in 1898 this was like the kind of key example
- of the usage of the Poisson distribution because, and
- it was used to model the number of soldiers that were kicked by
- horses in the Prussian War.
- Now the Poisson distribution is useful for
- modeling rare events, I’m very glad to hear that it’s
- rare to be kicked by a horse in the Prussian War.
- Now here’s the PMF, this is the PMF for
- the Poisson distribution.
- And you should think to yourself that this looks familiar,
- because it looks very similar to the binomial distribution.
- It looks kind of like a shifted and
- squished version of the binomial, and it should,
- given that it is a limiting version of the binomial.
- Now it’s useful for modeling waiting times for
- independent events.
- You could think about n is being like little time intervals, and
- p is being the probability of success in each
- little time interval.
- And so as the interval gets smaller there are a lot of them
- and the probabilities get smaller at the same rate.
- Now, let me give you a sort of a more modern example of
- the Poisson Distribution than getting kicked by a horse,
- which is the number of emails that I get per hour.
- So, I get about seven emails per hour.
- So, I’ll be completely honest I get much, much, much,
- more than seven emails per hour.
- But seven is the number of
- emails that I actually have to respond to.
- So what I did was I kept track of how many emails that I get
- every hour for a whole week.
- So this is just the number of emails that require a response.
- And you’re thinking I still couldn’t possibly
- answer that many emails, and you’re right but I do my best.
- So for each hour, I counted the number of emails I got in that
- hour and I tallied them all up, and it looks like this.
- So what that means is that there were seven hours in which
- I got eight emails in that hour.
- And the cool thing about this, is it looks very much like
- the Poisson distribution with lambda = 7, which is great.
- So that’s a really good example you can remember of a Poisson
- distribution, and that’s our introduction to the Poisson.
- End of transcript. Skip to the start.