University of Waterloo

ACTSC 232: Intro to Actuarial Mathematics

Week 1 video

ACTSC 232: Intro to Actuarial Mathematics

Week 1 video

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University of Waterloo

ACTSC 232: Intro to Actuarial Mathematics

Week 1 video

ACTSC 232: Intro to Actuarial Mathematics

Week 1 video

Просмотров: 9529

October 23, 2010 - Professor Margot Gerritsen illustrates how mathematics and computer modeling influence the design of modern airplanes, yachts, trucks and cars. This lecture is offered as part of the Classes Without Quizzes series at Stanford's 2010 Reunion Homecoming.

Margot Gerritsen, PhD, is an Associate Professor of Energy Resources Engineering, with expertise in mathematical and computational modeling of energy and fluid flow processes. She teaches courses in energy and the environment, computational mathematics and computing at Stanford University.

Stanford University:

http://www.stanford.edu/

Stanford Alumni Association:

http://www.stanfordalumni.org/

Department of Mathematics at Stanford:

http://math.stanford.edu/

Margot Gerritsen:

http://margot.stanford.edu/

Stanford University Channel on YouTube:

http://www.youtube.com/stanford

Margot Gerritsen, PhD, is an Associate Professor of Energy Resources Engineering, with expertise in mathematical and computational modeling of energy and fluid flow processes. She teaches courses in energy and the environment, computational mathematics and computing at Stanford University.

Stanford University:

http://www.stanford.edu/

Stanford Alumni Association:

http://www.stanfordalumni.org/

Department of Mathematics at Stanford:

http://math.stanford.edu/

Margot Gerritsen:

http://margot.stanford.edu/

Stanford University Channel on YouTube:

http://www.youtube.com/stanford

Просмотров: 668698

http://science.nd.edu

Studying mathematics, statistics and business can lead to certification as an actuary. Today's actuaries help make critical business decisions in a surprising variety of areas.

Learn more from from the experts, David E. Delahanty, ASA, and Nicole Delahanty, FSA, CIMA, who spoke at the Ask the Actuaries seminar on November 27, 2012.

Studying mathematics, statistics and business can lead to certification as an actuary. Today's actuaries help make critical business decisions in a surprising variety of areas.

Learn more from from the experts, David E. Delahanty, ASA, and Nicole Delahanty, FSA, CIMA, who spoke at the Ask the Actuaries seminar on November 27, 2012.

Просмотров: 30817

This video forms part of a mathematics course on Probability & Statistics by Prof David Spiegelhalter held at AIMS South Africa in 2012.

Please visit video-courses.aims.ac.za to download the supporting booklet.

Please visit video-courses.aims.ac.za to download the supporting booklet.

Просмотров: 6088

Taught by Dr. Greg Morrow from UCCS in Colorado

Просмотров: 1938

MIT 6.262 Discrete Stochastic Processes, Spring 2011

View the complete course: http://ocw.mit.edu/6-262S11

Instructor: Robert Gallager

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

More courses at http://ocw.mit.edu

View the complete course: http://ocw.mit.edu/6-262S11

Instructor: Robert Gallager

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

More courses at http://ocw.mit.edu

Просмотров: 74941

Linear Models taught by Dr. Greg Morrow from UCCS.

**NOTE: There is no Lecture 1**

Methods and results of linear algebra are developed to formulate and study a fundamental and widely applied area of statistics. Topics include generalized inverses, multivariate normal distribution and the general linear model. Applications focus on model building, design models, and computing methods. The Statistical Analysis System (software) is introduced as a tool for doing computations.

**NOTE: There is no Lecture 1**

Methods and results of linear algebra are developed to formulate and study a fundamental and widely applied area of statistics. Topics include generalized inverses, multivariate normal distribution and the general linear model. Applications focus on model building, design models, and computing methods. The Statistical Analysis System (software) is introduced as a tool for doing computations.

Просмотров: 3377

WHAT IS STATISTICS?

o The mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling

o The subject of statistics can be divided into descriptive statistics - describing data, and inferential Statistics - drawing conclusions from data (Source: dictionary.com)

WHY SHOULD WE STUDY STATISTICS?

Descriptive Statistics : To describe a phenomenon

o Summary and presentation of data

Inferential Statistics: To draw conclusions

o Making statements or predictions about the population based on statistical information

POPULATION & SAMPLE

POPULATION: is the group of all objects or individuals of interest.

o All York Students

o Canadians

SAMPLE: is a subset of the population

o 40 York students chosen at random

o People interviewed for the latest election poll

o We refer to the individual components of a sample as "observations"

PARAMETERS AND STATISTICS

Very generally we can say that:

o Populations are described by PARAMETERS

o Samples are described by STATISTICS

For example:

Parameter: the average hair length of all domestic cats (reflects the true value for the population)

Statistic: the average hair length of cats in my sample (it's an estimate)

Statistical inference: is the process of drawing a conclusion about the population based on the sample (with certain levels of confidence and significance)

FINAL DEFINITIONS

A variable is a characteristic of a population or sample.

o student grades, height, income, etc.

Variables have values

o student marks (0..100)

Data are the observed values of a variable.

o student marks: {67, 74, 71, 83, 93, 55, 48}

ATTAINING THE DATA

We have a phenomenon of interest and we would like to collect data to study it further

o We can directly collect the data: this is called PRIMARY DATA.

o We can use data collected by others (e.g. Statistics Canada; market research companies; etc.): this is called SECONDARY DATA

o

HOW DO WE COLLECT PRIMARY DATA?

1. By observations

2. By experiment

3. By survey

The difference is generally in the amount of control exercised by the researcher and the strength of the inference that can be made

DECISIONS INVOLVED IN SAMPLING

Sample Population

o From which population do we sample?

o Why is this important? What do we have to consider?

Sample Size

o How large should the sample be?

Sampling Method

o How should we pick the sample out of the population?

SAMPLE SIZE DEPENDS ON

o The size of the population

The sample size will INCREASE with the population size

o The variation in the population

The sample size will INCREASE with the variation

o The amount of error that can be tolerated

The sample size will DECREASE with the accepted error

o The amount of resources available

The sample size will INCREASE with resources

HOW TO CREATE THE SAMPLE

There are several statistical sampling methods you can use:

1. Simple Random Sample

2. Stratified Random Sample

3. Cluster Sample

SIMPLE RANDOM SAMPLE (SRS)

Each subject is equally likely to be chosen

o Like raffles, drawing from a hat, etc.

o Subject choice is determined by random numbers

STRATIFIED RANDOM SAMPLE

The population is divided into mutually exclusive subgroups called strata

o i.e. age, gender, home type

Within strata, the sampling is random (simple)

Advantages: Assures the sample has the same structure as the population

Inferences can also be made about the subcategories

CLUSTER SAMPLING

The population is divided into groups, called clusters

Geographical regions, classrooms in a school

Each clusters ideally has the same characteristics as the population

We use simple random sampling to select only a few clusters

We then use either simple random or stratified sampling within each cluster

SAMPLING ERRORS

A sampling error refers to the difference between the sample statistic and the population parameter

Example: survey shows 51% of students work when in fact only 50.42% work

We will learn how to deal with this error in later classes

NON-SAMPLING ERRORS

A non-sampling Error refers to errors in data acquisition Inaccuracies & mistakes; less-than-truthful responses

Non-response Bias: only people with a certain agenda respond to the survey

Selection bias: sampling problems

o The mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling

o The subject of statistics can be divided into descriptive statistics - describing data, and inferential Statistics - drawing conclusions from data (Source: dictionary.com)

WHY SHOULD WE STUDY STATISTICS?

Descriptive Statistics : To describe a phenomenon

o Summary and presentation of data

Inferential Statistics: To draw conclusions

o Making statements or predictions about the population based on statistical information

POPULATION & SAMPLE

POPULATION: is the group of all objects or individuals of interest.

o All York Students

o Canadians

SAMPLE: is a subset of the population

o 40 York students chosen at random

o People interviewed for the latest election poll

o We refer to the individual components of a sample as "observations"

PARAMETERS AND STATISTICS

Very generally we can say that:

o Populations are described by PARAMETERS

o Samples are described by STATISTICS

For example:

Parameter: the average hair length of all domestic cats (reflects the true value for the population)

Statistic: the average hair length of cats in my sample (it's an estimate)

Statistical inference: is the process of drawing a conclusion about the population based on the sample (with certain levels of confidence and significance)

FINAL DEFINITIONS

A variable is a characteristic of a population or sample.

o student grades, height, income, etc.

Variables have values

o student marks (0..100)

Data are the observed values of a variable.

o student marks: {67, 74, 71, 83, 93, 55, 48}

ATTAINING THE DATA

We have a phenomenon of interest and we would like to collect data to study it further

o We can directly collect the data: this is called PRIMARY DATA.

o We can use data collected by others (e.g. Statistics Canada; market research companies; etc.): this is called SECONDARY DATA

o

HOW DO WE COLLECT PRIMARY DATA?

1. By observations

2. By experiment

3. By survey

The difference is generally in the amount of control exercised by the researcher and the strength of the inference that can be made

DECISIONS INVOLVED IN SAMPLING

Sample Population

o From which population do we sample?

o Why is this important? What do we have to consider?

Sample Size

o How large should the sample be?

Sampling Method

o How should we pick the sample out of the population?

SAMPLE SIZE DEPENDS ON

o The size of the population

The sample size will INCREASE with the population size

o The variation in the population

The sample size will INCREASE with the variation

o The amount of error that can be tolerated

The sample size will DECREASE with the accepted error

o The amount of resources available

The sample size will INCREASE with resources

HOW TO CREATE THE SAMPLE

There are several statistical sampling methods you can use:

1. Simple Random Sample

2. Stratified Random Sample

3. Cluster Sample

SIMPLE RANDOM SAMPLE (SRS)

Each subject is equally likely to be chosen

o Like raffles, drawing from a hat, etc.

o Subject choice is determined by random numbers

STRATIFIED RANDOM SAMPLE

The population is divided into mutually exclusive subgroups called strata

o i.e. age, gender, home type

Within strata, the sampling is random (simple)

Advantages: Assures the sample has the same structure as the population

Inferences can also be made about the subcategories

CLUSTER SAMPLING

The population is divided into groups, called clusters

Geographical regions, classrooms in a school

Each clusters ideally has the same characteristics as the population

We use simple random sampling to select only a few clusters

We then use either simple random or stratified sampling within each cluster

SAMPLING ERRORS

A sampling error refers to the difference between the sample statistic and the population parameter

Example: survey shows 51% of students work when in fact only 50.42% work

We will learn how to deal with this error in later classes

NON-SAMPLING ERRORS

A non-sampling Error refers to errors in data acquisition Inaccuracies & mistakes; less-than-truthful responses

Non-response Bias: only people with a certain agenda respond to the survey

Selection bias: sampling problems

Просмотров: 47029

The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves.

View the complete course: http://ocw.mit.edu/18-03S06

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

More courses at http://ocw.mit.edu

View the complete course: http://ocw.mit.edu/18-03S06

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

More courses at http://ocw.mit.edu

Просмотров: 686583

An overview of some of the basic concepts and problem types in statistics and probability for the IB Math standard level course. If you want to follow along and do the problems, please download the handout at https://docs.google.com/open?id=0B6hD-LURYkgEYWI4NThkN2QtMDk3OC00YTI4LWI4YTEtMzUxYWRiMzRhM2Yx . This video is neither produced by nor endorsed by the IB.

Просмотров: 34754

In celebration of Year of Science, Langara College held a Careers in Science Speakers Series. This one is Mathematics & Statistics specific.

Speakers: David McGowan and Michael Wach

Dave grew up on the mean streets of Winnipeg before moving West to Kelowna where he attended Okanagan University College (now UBC Okanagan), receiving a Bachelors of Science degree in physics and math. Dave is a consulting actuary at Towers Watson, a global management consulting firm, where he consults to large corporations on the financial management of their post-retirement benefits plans. Despite several allegations, his performance enhancing drug use has never been proven.

Michael is an actuary with 10 years of experience in the human resource consulting industry. He is a consultant at Towers Watson where he helps clients manage the financial implications of their benefit plans. Michael has a Bachelor of Science degree in Actuarial Mathematics from the University of Manitoba. Contrary to various news reports, Michael was not responsible for the economic collapse of 2008.

Speakers: David McGowan and Michael Wach

Dave grew up on the mean streets of Winnipeg before moving West to Kelowna where he attended Okanagan University College (now UBC Okanagan), receiving a Bachelors of Science degree in physics and math. Dave is a consulting actuary at Towers Watson, a global management consulting firm, where he consults to large corporations on the financial management of their post-retirement benefits plans. Despite several allegations, his performance enhancing drug use has never been proven.

Michael is an actuary with 10 years of experience in the human resource consulting industry. He is a consultant at Towers Watson where he helps clients manage the financial implications of their benefit plans. Michael has a Bachelor of Science degree in Actuarial Mathematics from the University of Manitoba. Contrary to various news reports, Michael was not responsible for the economic collapse of 2008.

Просмотров: 1395

Taught by Dr. Greg Morrow from University of Colorado in Colorado Springs

Просмотров: 725

Lecture 1: The Geometry of Linear Equations.

View the complete course at: http://ocw.mit.edu/18-06S05

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

More courses at http://ocw.mit.edu

View the complete course at: http://ocw.mit.edu/18-06S05

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

More courses at http://ocw.mit.edu

Просмотров: 1223349

Lecture by Professor Andrew Ng for Machine Learning (CS 229) in the Stanford Computer Science department. Professor Ng provides an overview of the course in this introductory meeting.

This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include supervised learning, unsupervised learning, learning theory, reinforcement learning and adaptive control. Recent applications of machine learning, such as to robotic control, data mining, autonomous navigation, bioinformatics, speech recognition, and text and web data processing are also discussed.

Complete Playlist for the Course:

http://www.youtube.com/view_play_list?p=A89DCFA6ADACE599

CS 229 Course Website:

http://www.stanford.edu/class/cs229/

Stanford University:

http://www.stanford.edu/

Stanford University Channel on YouTube:

http://www.youtube.com/stanford

This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include supervised learning, unsupervised learning, learning theory, reinforcement learning and adaptive control. Recent applications of machine learning, such as to robotic control, data mining, autonomous navigation, bioinformatics, speech recognition, and text and web data processing are also discussed.

Complete Playlist for the Course:

http://www.youtube.com/view_play_list?p=A89DCFA6ADACE599

CS 229 Course Website:

http://www.stanford.edu/class/cs229/

Stanford University:

http://www.stanford.edu/

Stanford University Channel on YouTube:

http://www.youtube.com/stanford

Просмотров: 618620

Dr Robert Campbell of the Unviersity of St. Andrews, Scotland, gives a talk to PhD students about working as a "quant" in the finance industry. This was filmed 7th November 2008 and is part of a series of seminars supported by the UK's Economics Network. Slides can be downloaded from http://www.economicsnetwork.ac.uk/archive/standrews_phd/campbell_finance.htm

The Economics Network

Speaker: Dr Robert Campbell

The Economics Network

Speaker: Dr Robert Campbell

Просмотров: 13863

We introduce the Gamma distribution and discuss the connection between the Gamma distribution and Poisson processes.

Просмотров: 10627

Taught by Dr. Greg Morrow from University of Colorado in Colorado Springs

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At UCCS, our faculty, staff, and students are constantly reaching higher to achieve their goals. It's also a place where students are having fun, making new friends, and experiencing college life to the fullest, because we also understand that the things you do outside of class are an important part of the learning process.

Просмотров: 5606

This is the second of three videos concerned with statistics and probability. This is a complimentary video from Dave Pilmer that aligns with GED Prep Plus resource. Did you know you can download this free print resource from the NSSAL site? Search "FREE Math Resources" on YouTube for more information or go to http://gonssal.ca/General-Public/Documents-Resources/ALPLocalResources.shtml

Просмотров: 3409