Probability in R. Discrete Random Variables
3.8 (49 ratings)
2,333 students enrolled
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# Probability in R. Discrete Random Variables

Infermath links mathematical theory with programming application to give high level understanding of quantitative fields
3.8 (49 ratings)
2,333 students enrolled
Created by Pawel Dudko
Last updated 5/2017
English
Price: Free
Includes:
• 2 hours on-demand video
• 2 Supplemental Resources
• Access on mobile and TV
• Certificate of Completion
What Will I Learn?
• draw random numbers in R
• use descriptive statistics in R
• use boolean variables in R
• define and use Bernoulli random variable
• define and derive probability of binomial distribution
• define and assign values to vectors
• use histogram in R
• use combinations in set theory
• define and assign values to matrices in R
• draw plots in R
• use for and while loops in R
• use logical conditions in R
• sum geometric series
• define and derive probability of geometric distribution
• predict numerical limitations of computers and R
• define functions in R
• define infinite series of events
• specify conditions for series convergence
• use independence of events
• use properties of complementary events
• use squeeze theorem
• hold the loop execution and print results in R
• define and prove Borel-Cantelli lemma
View Curriculum
Requirements
• high school calculus
• high school probability theory
Description

Probability in R is a course that links mathematical theory with programming application. Discrete Random Variables series gives overview of the most important discrete probability distributions together with methods of generating them in R. Fundamental functionality of R language is introduced including logical conditions, loops and descriptive statistics. Viewers are acquainted with basic knowledge of numerical analysis.

Course is designed for students of probability and statistics who would like to enrich their learning experience with statistical programming. While basic knowledge of probability and calculus is useful prerequisite it is not essential. The suggested method of using the course is by repeating the reasoning and replicating the R code. Therefore it is essential for students to download and use R in the course.

The course consists of twelve short lectures totaling two hours of video materials. Four major topics are covered: Bernoulli distribution (2 lectures), binomial distribution (3 lectures), geometric distribution (3 lectures) and Borel-Cantelli lemma (4 lectures). Eight lectures are presented in a form of writing R code. Remaining four lectures focus solely on theory of probability.

How is Infermath different from other education channels? It equips students with tools and skills to use acquired knowledge in practice. It aims to show that learning mathematics is not only useful but also fun and inspiring. It places emphasis on equal chances in education and promotes open source approach.

Who is the target audience?
• students of probability theory
• R and statistical programming students
• bachelor students of quantitative fields
• high school students
• open source enthusiasts
• programming beginners
• self learners
• classical music melomaniacs
• inquisitive souls
• philosophy and logic apprentices
Compare to Other R Courses
Curriculum For This Course
13 Lectures
02:03:56
+
Bernoulli random variable
2 Lectures 18:42

Infermath links mathematical theory with programming application to provide high level understanding of quantitative fields.

Introduction
12:03

In this video we generate a Bernoulli random variables using R. We familiarize ourselves with boolean variables and logical conditions in R.
Bernoulli distribution
06:39
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Binomial distribution
3 Lectures 28:58
We define binomial distribution and generate it using R. We familiarize ourselves with histogram in R.
Binomial distribution 1
06:32

In this episode we derive the probability of each outcome in binomial distribution. We show the probabilities add up to 1 using set theory, polynomials and Pascal's triangle.
Binomial distribution 2
12:42

In this video we are comparing the probability distribution of binomial random variables to simulation in R. We learn how to generate vectors and matrices, use the for loop and bar plot in R.

Binomial distribution 3
09:44
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Geometric distribution
3 Lectures 25:23
We define geometric distribution and draw random variables from it in R. We familiarize ourselves with while loop and scientific notation.
Geometric distribution 1
07:31

We derive probability distribution of the geometric random variables and learn about geometric series. We encounter cumulative distribution function.
Geometric distribution 2
09:23

We want to increase to infinity the maximum value coming from geometric distribution. On our way we encounter NAs and machine epsilon but don't give up.

Geometric distribution 3
08:29
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Borel-Cantelli lemma
4 Lectures 40:57
We create a function in R returning a result of Bernoulli trial and we use it in for loop to generate series of trials. We try to understand what does it mean for a series of events to happen infinitely many times.
Borel-Cantelli lemma 1
09:22

We derive the first part of the Borel - Cantelli lemma. On the way we use properties of sequences and series, visit police station and do a quick trip to outer space.
Borel-Cantelli lemma 2
08:29

We prove the second part of Borel-Cantelli lemma. We come across exponential function, complementary events, a monkey and William Shakespeare.
Borel-Cantelli lemma 3
10:15

In the last episode of discrete random variables we use Borel-Cantelli lemma to generate infinite series of successful Bernoulli trials. As we approach infinity we turn to philosophy and music.
Borel-Cantelli lemma 4
12:51
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Application
1 Lecture 09:56
Application in Financial Engineering: Binomial Tree
09:56