Mathematical (Actuarial) Statistics:(Exam P/Ct3/Cs1)

By MJ the Fellow Actuary

What you'll learn
A solid understanding of statistics and a good foundation of models, correlation and hypothesis testing.
Requirements
Must be comfortable with Maths and patient as these concepts can be tricky.
Description
Statistics is all about processing data and extracting information. The information we seek is the parameters and distribution of the random variable that generated the data. Armed with this information we can answer questions about reality and optimize industrial processes. Statistics thus forms the backbone of science and business and this course is designed to help you understand the components of this fundamental subject and how they all fit together. Designed for Actuaries, but applicable for everyone. This course contains the new sections for the CS1 exam.Sections:Exploratory Data AnalysisGeneral Probability TheoryRandom VariablesProbability DistributionsGenerating FunctionsJoint Distributions (Covariance)Conditional ExpectationsCentral Limit TheoremSampling and Statistical InferencePoint EstimationConfidence IntervalsHypothesis TestingLinear Regression and CorrelationAnalysis of VarianceBayesian Statistics and Credibility TheoryStudent QuestionsIntroduction to R Programming

Overview

Section 1: Exploratory Data Analysis

Lecture 1 Introduction to Exploratory Data Analysis

Lecture 2 Graphical Representation of Data

Lecture 3 Data Location

Lecture 4 Spread of Data

Lecture 5 Symmetry and Skewness

Lecture 6 Exam Question

Section 2: General Probability Theory

Lecture 7 Introduction to Probability Theory

Lecture 8 Set Theory

Lecture 9 Venn Diagrams

Lecture 10 Probability

Lecture 11 Conditional Probability

Lecture 12 Easy Exam Question 1

Lecture 13 Easy Exam Question 2 (Venn Diagrams)

Lecture 14 Easy Exam Question 3 (Probability Tables)

Lecture 15 Difficult Exam Question

Section 3: Random Variables

Lecture 16 Introduction to Random Variables

Lecture 17 Discrete Random Variables

Lecture 18 Continuous Random Variables

Lecture 19 Expected Values

Lecture 20 Functions of a Random Variable

Section 4: Probability Distributions

Lecture 21 Introduction to Distributions

Lecture 22 Discrete Probability Distributions

Lecture 23 Continuous Probability Distribution

Section 5: Generating Functions

Lecture 24 Introduction to Generating Functions

Lecture 25 Overview of Generating Functions

Lecture 26 Easy Exam Question

Section 6: Joint Distributions

Lecture 27 Introduction to Joint Distributions

Lecture 28 Joint Probability Functions

Lecture 29 Exam Quesiton

Section 7: Conditional Expectations

Lecture 30 Introduction to Conditional Expectations

Lecture 31 Conditional Expectations

Lecture 32 Conditional Variance

Lecture 33 Compound Distributions

Lecture 34 Moment Generating Functions of Compound Distributions

Lecture 35 Exam Question on MGF and Compound Distribution

Lecture 36 Exam Question on Conditional Distributions

Section 8: Central Limit Theorem

Lecture 37 Introduction to Central Limit Theorem

Lecture 38 History of the CLT and how it almost ended the world

Lecture 39 Applying the CLT and understanding how we got it

Lecture 40 Continuity Correction

Lecture 41 Exam Question on CLT

Section 9: Sampling and Statistical Inference

Lecture 42 Introduction to Sampling and Statistical Inference

Lecture 43 Jargon of Statistics

Lecture 44 Sample Mean

Lecture 45 Expected Value of the Sample Variance

Lecture 46 Variance of Sample Variance

Lecture 47 The t result

Lecture 48 The F result

Lecture 49 Exam Question on Sampling

Section 10: Point Estimation

Lecture 50 Introduction to Point Estimation

Lecture 51 Whats the Point of Point Estimation

Lecture 52 Method of Moments

Lecture 53 Method of Maximum Likelihood

Lecture 54 Properties of Estimators

Lecture 55 Cramer Rao Lower Bound

Section 11: Confidence Intervals

Lecture 56 Introduction to Confidence Intervals

Lecture 57 Confidence Intervals

Lecture 58 Pivotal Method of Confidence Intervals

Lecture 59 Pivotal Method for Variance

Lecture 60 Confidence Intervals for Discrete Distributions

Lecture 61 Confidence Intervals for Two Samples

Lecture 62 Confidence Interval for Two Population Variance

Lecture 63 Confidence Intervals for Paired Data

Lecture 64 Short Exam Question

Lecture 65 Long Exam Question

Section 12: Hypothesis Testing

Lecture 66 Introduction to Hypothesis Testing

Lecture 67 Hypothesis Testing

Lecture 68 Hypothesis Testing's link to Confidence Intervals

Lecture 69 Types of Errors in Hypothesis Testing

Lecture 70 Various Test Stats for Hypothesis Testing

Lecture 71 Goodness of Fit Test

Lecture 72 Contingency Tables for 2 Factor Independence Test

Lecture 73 Exam Question with Hypothesis Testing

Section 13: Linear Regression and Correlation

Lecture 74 Introduction to Linear Regression

Lecture 75 Regression

Lecture 76 Correlation role in Regression Analysis

Lecture 77 Sample Regression

Lecture 78 Linear Regression Model

Lecture 79 Goodness of Fit

Lecture 80 Slope Parameter

Lecture 81 Mean Response and Individual Predictions

Lecture 82 Residual Analysis

Lecture 83 Transformation

Lecture 84 Multiple Linear Regression

Section 14: Analysis of Variance

Lecture 85 Introduction to ANOVA

Lecture 86 ANOVA Basics

Lecture 87 ANOVA Exam Question

Section 15: Bayesian Statistics

Lecture 88 Visual Recap of Conditional Probability

Lecture 89 Bayesian Statistics Example

Lecture 90 Prior and Posterior Distributions

Lecture 91 Notation

Lecture 92 Prior and Posterior Example

Lecture 93 Conjugate Priors

Lecture 94 Loss Functions

Lecture 95 Credibility Theory

Lecture 96 Bayesian Credibility

Lecture 97 Empirical Bayes Credibility Theory

Lecture 98 Exam Question on EBCT

Section 16: Student Questions

Lecture 99 Whats the difference between a Statistic and a Parameter

Lecture 100 Null Hypothesis, what is it and why can't it be accepted

Section 17: R basics for Actuaries

Lecture 101 R basics for Actuaries - Part 1

Lecture 102 R basics for Actuaries - Part 2

University students and people trying to get into the Actuarial Profession.