Mathematical Actuarial StatisticsExam PCT3CS1
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.
Course Information:
Udemy | English | 13h 46m | 18.84 GB
Created by: Michael Jordan
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