Probability made easy: Expected value and variance

Expected value and variance
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  • Lectures 44
  • Length 2.5 hours
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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    Available on iOS and Android
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About This Course

Published 10/2015 English

Course Description

This course is a part in a series of courses that covers a complete course in probability theory taught in the US colleges.

In this course you will learn the notions of expected value and variance. You will learn how to predict the results of random events and how to predict how much on average the actual results would deviate from your estimate.

If you are looking for an efficient way to learn/review probability theory, this course is for you. With dynamic slides instead of slower handwriting, each hour of the series covers the material of more than a week of regular live lectures! Though it is not a replacement for a live course, it is a fantastic aid.

You may review lectures as many times as you want, skip easy exercises when the material is familiar, choose your own pace! If you need help, I will answer every single question you post on the discussion board. If you are not completely satisfied, I offer a 30 day money back guarantee.

What is in the package:

  • more than 20 theoretic video lectures and lectures with motivations,
  • 19 practice video lectures marked as easy, intermediate and advanced,
  • more than 60 pages of transcripts of video lectures,
  • hundreds of slides,
  • paradoxes, jokes, and, of course,
  • my help (post your questions on the board!).

What are the requirements?

  • familiarity with fundamental notions such as outcomes, events and probability would be helpful (these notions are briefly reviewed in the first section)

What am I going to get from this course?

  • learn how to predict the results of random events (expected value)
  • learn how to predict how much on average the actual results would deviate from your estimate (standard deviation)

What is the target audience?

  • students who would like an efficient tutorial

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Section 1: Introduction
Introduction
Preview
02:58
Section 2: Review
Review: Sample spaces and distribution functions
Preview
02:47
Uniform distribution
01:34
Review: Random variables
02:28
Review: Binomial coefficients
02:38
Section 3: Classical random variables
Binomial distribution
06:34
Problem solving (easy)
03:42
Geometric random variable
04:03
Problem solving (easy)
03:28
Negative binomial distribution
08:41
Problem solving (easy)
01:13
Poisson distribution
07:14
Problem solving (easy)
03:54
Problem solving (warning)
02:50
Section 4: Expected value
Expected value (motivation)
02:38
Expected value (definition)
02:15
Problem solving (easy)
03:52
Problem solving (intermediate)
Preview
03:22
Problem solving (advanced)
06:00
Functions of random variables. Problem solving (easy)
04:29
Expected values of sums of random variables
05:02
Expected values of products of random variables
03:44
Expected values of sums and products: Warning
05:28
Expected values of sums of random variables: Proof
03:51
Expected values of products of random variables: Proof
03:13
Section 5: Variance
Variance of random variables: Motivation
02:53
Variance of a random variables: Definition
01:48
Problem solving (easy)
04:36
Properties of variance
02:54
Problem solving (warning)
01:59
Problem solving (easy)
02:17
Problem solving (intermediate)
04:07
Proof of the first property of the variance
02:07
Section 6: Expected value and variance of classical random variables
Classical random variables: Binomial random variable
01:10
Problem solving (easy)
02:03
Binomial random variable. Proof of the formulas
04:39
Classical random variables: Geometric random variable
02:02
Problem solving (easy)
02:05
Problem solving (intermediate)
Preview
02:01
Problem solving: Negative binomial random variable
02:31
Classical random variables: Poisson random variable
01:25
Problem solving (easy)
01:12
Problem solving (advanced)
03:37
Section 7: Thank you!
Thank you!
1 page

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Instructor Biography

I am a professional mathematician. As a mathematician I worked in US, Mexico, Japan, Canada and Germany. I am an author of 16 research papers published in internationally renowned journals.

I taught courses ranging from middle school to PhD level, including such high level courses as Topological Quantum Field Theory, Moduli spaces of Riemann curves, and Topological Surgery Theory.

What you may expect from me is a well structured course with clearly explained notions and theory.


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