English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 73 Lessons (10h 37m) | 9.98 GB
Master the Further Statistics 1 content from A-level Further Maths, and practice on real past paper exam questions.
A-Level Further Maths: Further Statistics 1 is a course for anyone studying A-Level Further Maths who has chosen the Further Statistics 1 module.
This course covers all the content in the Further Statistics 1 paper. The course has been modelled around the Edexcel exam board. Some of the topics covered here appear in other boards, but it’s not designed with them in mind . It is, however, a great option for anyone looking to learn more advanced probability and statistics.
The main sections of the course are:
– Discrete Random Variables – we expand what we already know abot discrete random variables, learning how to find expectation and variance.
– The Poisson Distribution – we will learn a brand new discrete distribution and learn how to solve a range of questions relating to it, as well as how to find Poisson approximations of binomial distributions.
– Geometric and Negative Binomial Distributions – we will learn 2 more discrete distributions and learn how to solve questions about these.
– Hypothesis Testing – we’ll look at how to test hypotheses relating to the Poisson and Geometric Distributions.
– The Central Limit Theorem – we’ll explore this fascinating result and see how to use it solve some quite advanced problems.
– Chi Squared Tests – we’ll learn how to test whether data is well modelled by a distribution, and how to test for association.
– Probability Generating Functions – we’ll learn what probability generating functions are and how to construct them for all the discrete distributions we know.
– Quality of Tests – we’ll learn what Type I and Type II errors are, what statistical power is, and how to create a power function.
What you get in this course:
Videos: Watch as I explain each topic, introducing all the key ideas, and then go through a range of different examples, covering all the important ideas in each. In these videos I also point out the most common misconceptions and errors so that you can avoid them.
Quizzes: Each sub-section is followed by a short quiz for you to test your understanding of the content just covered. Most of the questions in the quizzes are taken from real A-Level past papers. Feel free to ask for help if you get stuck on these!
Worksheets: At the end of each chapter I have made a collection of different questions taken from real A-Level past papers for you to put it all together and try for yourself. At the bottom of each worksheet is a full mark-scheme so you can see how you have done.
What you’ll learn
- Discrete Random Variables
- The Poisson Distribution
- Geometric and Negative Binomial Distributions
- Hypothesis Testings
- The Central Limit Theorem
- Chi Squared Tests
- Probability Generating Functions
- Quality of Tests
Who this course is for:
- People studying A-Level Further Maths
- People who want to learn some more advanced probability and statistics
Table of Contents
Introduction
1 Introduction
2 AS vs A-Level Content
Discrete Random Variables
3 Expectation of a Discrete Random Variable – Part 1
4 Expectation of a Discrete Random Variable – Part 2
5 Variance of a Discrete Random Variable
6 Discrete Random Variables with Functions of X – Part 1
7 Discrete Random Variables with Functions of X – Part 2
8 Discrete Random Variables – Exam Questions
9 Discrete Random Variables – Exam Question Pack
The Poisson Distribution
10 The Poisson Distribution – Introduction
11 Conditions for Using the Poisson Distribution
12 Poisson Distribution – Calculator Use
13 Different Intervals
14 Sums of Poisson Distributions
15 Expectation and Variance of Poisson Distributions
16 Expectation and Variance of a Binomial Distribution
17 Poisson Approximations to Binomial Distributions
18 Poisson Distribution – Exam Questions
19 Optional – Derivation of Poisson Distribution Formula
20 Poisson Distribution – Exam Question Pack
The Geometric and Negative Binomial Distributions
21 The Geometric Distribution – Introduction
22 Conditions for Using The Geometric Distribution
23 The Geometric Distribution – Calculating Probabilities
24 The Geometric Distribution – Working Backwards
25 Expectation and Variance of Geometric Distributions
26 The Negative Binomial Distribution
27 Expectation and Variance of the Negative Binomial Distribution
28 Geometric and Negative Binomial Distributions – Exam Questions
29 Optional – Proof of Expectation and Variance of Geometric Distributions
30 Geometric and Negative Binomial Distributions – Exam Question Pack
Hypothesis Testing
31 Poisson Hypothesis Tests
32 Poisson Critical Regions
33 Geometric Distribution Hypothesis Tests
34 Geometric Distribution Critical Regions
35 Hypothesis Testing – Exam Question Pack
The Central Limit Theorem
36 The Distribution of Sample Means
37 The Central Limit Theorem – Introduction
38 The Central Limit Theorem – Calculating Probabilities
39 The Central Limit Theorem and Standard Distributions
40 The Central Limit Theorem – Exam Questions
41 Optional – When the Central Limit Theorem Fails
42 The Central Limit Theorem – Exam Questions
Chi Squared Tests
43 The Chi Squared Distributions
44 Chi Squared Hypothesis Tests – Part 1
45 Chi Squared Hypothesis Tests – Part 2
46 Two Formulas for Chi Squared
47 Grouping
48 Testing Given Distributions
49 Estimating parameters
50 Contingency Tables – Part 1
51 Contingency Tables – Part 2
52 Chi Squared Tests for Geometric Distributions
53 Chi Squared Tests – Exam Questions
54 Chi Squared Tests – Exam Question Pack
Probability Generating Functions
55 Probability Generating Function Introduction
56 PGFs of Standard Functions – Part 1
57 PGFs of Standard Functions – Part 2
58 Expectation and Variance of a PGF – Derivation
59 Expectation and Variance of a PGF
60 Expectation and Variance of Standard Distributions
61 Sums of Independent Random Variables – Part 1
62 Sums of Independent Random Variables – Part 2
63 Probability Generating Functions – Exam Questions
64 Probability Generating Functions – Exam Question Pack
Quality of Tests
65 Type I and Type II Errors
66 Type I and Type II Errors with the Normal Distribution – Part 1
67 Type I and Type II Errors with the Normal Distribution – Part 2
68 Type I and Type II Errors with the Normal Distribution – Part 3
69 Size and Power of a Test
70 The Power Function – Part 1
71 The Power Function – Part 2
72 Quality of Tests – Exam Questions
73 Quality of Tests – Exam Question Pack
Resolve the captcha to access the links!
