# Advanced statistics teaching resources: Continuous random variables

Resources and ideas for mathematics, advanced statistics, continuous random variables, written by teachers to support teaching and learning

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#### Hypothesis Test for a Population Mean - Analogy to a Criminal Trial

This is a student workbook that can supplement lessons on hypothesis tests for a population mean. I teach the stages of hypothesis testing using analogies to a criminal trial. My students like this comparison; they are more engaged and it helps them to see the relevance of the different stages. Once students are confident with the terminology, we create our own courtroom in the classroom and role-play the stages of hypothesis testing with students acting as the jury, prosecution, judge and defence.Contents of the workbook1. A summary of the 5 stages of hypothesis testing2. A detailed analogy to a criminal trial3. One worked example4. Space for students to complete their own examples.5. Worksheets on:a. the null and alternative hypothesisb. type I and type II errorsc. checking assumptionsd. sampling distributionse. the normal distributionf. the t-distributiong. interpreting p-valuesAnswers for worksheets provided in separate document. The preview file shows a selection of pages from the workbook.

#### A-level (Post 16) Statistics Revision Worksheets

These worksheets are useful revision aids that include mixed questions to different a-level statistic topics. Solution sheets are provided.

#### Distribution Comparison: Normal, Poisson, Binomial

Allows the user (teacher or pupil) to easily show a specific distribution. E.g. Normal, Poisson or Binomial and compare distribution approximations
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#### Statistics: Complete (S1) Bundle - designed for Edexcel, but suitable for all S1 courses

Designed to teach all the main aspects of the S1 statistics course. Designed for the Edexcel syllabus, but suitable for all different S1 syllabus's. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thanks.

#### Statistics 1 Normal Distribution

Another great lesson from Lisa McNulty.
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#### Statistics and Probability

Discrete and continuous random variables, expectation algebra, chi-squares and goodness of fit, hypothesis testing, confidence levels CLT and distribution of sample means..

#### Uniform, exponential and normal distributions.

Definition of continuous probability distributions. Examples and theory on the uniform, exponential and normal distribution.
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#### Statistics 2

This bundle includes all the topics needed to cover the S2 AQA course including; Discrete and Continuous Random Variables Poisson Distribution Estimation Hypothesis Testing Chi-squared
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#### Calculus Option IB HL Mathematics

Set of class activities, lesson plans, power points, tests, trial exam for IB HL Maths Calculus Option.

#### Continuous Random Variable

Presentation that explains what a continuous random variable and the difference between a probability density function and a continuous distribution function. The presentation also covers median, quartiles, mean, variance and standard deviation.SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.

#### The Normal Distribution quiz

a short, multiple choice quiz to make sure pupils fully understand what is meant by notation and can see which part of the graph it represents.
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#### Statistics: (S2) Linear Adjustments / Combinations - 4 Lessons + Handout

This teaching PowerPoint contains 4 whole lessons!Lesson 1: Linear adjustment of random variablesLesson 2: Linear Combinations of random variablesLesson 3: Linear combinations for normal distributionsLesson 4: Linear combinations for Poisson distributions+ Rule sheet HANDOUTThese lessons are very structured, with clear lesson objectives, clear examples and small activities to build understanding of what linear adjustments/combinations do and why the rules are the way they are. The lessons do link to a textbook that I use, however, for copyright reasons I can not publish these exercises, but this is easily substituted for another textbook that you use to accompany your course. I have found these PowerPoints to be very effective in teaching this topic. NOTE: Feel free to browse my shop for more free and premium resources and as always please rate and feedback, thanks.

#### Introduction to Binomial Distribution

This was created, based on a class who have already been introduced to the Binomial Expansion. It's an introductory lesson following on from Random Discrete Variables.

#### Statistics: (S1) Coding or making the variance or mean easier (+ rule sheet)

This is a teaching resource to help pupils understand coding and the basics of linear adjustments/combinations and how to calculate back and forward from the original data to the coded data. It comes with a good starter, a look at re-arranging and then why coding is used and how it is used. Links to past exam questions, however, it does not come with lots of questions as at that point of practice, I use our S1 textbook. Also a rule sheet handout!NOTE: Feel free to browse my shop for more free and premium resources and as always please rate and feedback, thanks.

#### Statistics 2 - Hypothesis testing, worksheet.

Hypothesis testing worked examples worksheet.

#### Revision activity for Alevel statistics

The questions can be stuck on the classroom walls at random. pupils can start at any question and when they find the answer to the chosen question then they can go to the question which the answer is written on the top left hand side of the sheet. If they are successful in answering all the questions correctly, they finish with the question which they have started with.Other topics covered: Revision

#### S1 Normal Distribution Slides Edxcel

Page References from Pearson S1 text book

#### Normal Distribution Tarsia Jigsaw Puzzle

8 Question Tarsia Jigsaw covering using the Normal Distribution tables. Covers greater than, less than, and between questions with both positive and negative z scores…… There’s a guide to Tarsia here: http://www.tes.co.uk/article.aspx?storyCode=6107407

#### Discrete Random Variables

Worksheets on DRV including expectation and variance

#### A2 Full notes for Continuous Random Variables

***IF YOU LIKE THIS PLEASE CHECK OUT MY OTHER UNITS FOR A2 MATHS. BUY EACH UNIT SEPARATELY OR GET THE WHOLE PACK FOR £10!***These are my teaching notes for the CIE A2 Statistics Continuous Random Variable Unit. They include:- Explanation of Continuous Random Variables- Calculating Median, Mean, Variance and Quartiles using Continuous Random VariablesI've also included a summary diagram of the three distributions and when to use them to approximate.Notes include examples and explanations - essentially everything you would hope your students to copy down during the unit. The textbook exercise references are for the Nelson Mathematics Probability and Statistics Text (978-1-4085-1563-1). Which I highly recommend as an excellent text and which as been endorsed by Cambridge.Great for beginning teachers and also useful for students who are absent as you can print out a copy for their notes.

#### Normal Distribution Question sheets

With brief solutions

#### Binomial Distribution Revision Quiz. Worksheet.

I have used this quiz at the end of my lessons on the Binomial Distribution. I gave a copy of the quiz to each student, I split them into teams and asked randomly the questions on the sheet. Each team would get different points based on the difficulty of the question. The students enjoyed the activity a lot. If you run out of time, tell them to complete all the questions as homework.

#### Statistics 1 - Normal Distribution - KS4 and S1

The following sheet is an activity that explores the normal distribution function. Ideal for KS4 and Post16 students. Norm Dist 1 - explores how the mean and standard deviation effect the normal distribution function Norm Dist 2 - explores the probability distribution for a symmetrical two tailed event Norm Dist 3 - explores the probability of a general two tailed event You will need to allow macros to run when using most of the sheets available here. This can be checked by opening Excel and clicking :- Tools Macros Security and choosing Medium or Low security.

#### Normal Distribution Curve

This is a powerpoint I made for a lesson on using the standard Normal distribution to calculate probabilities by first finding the standardised scores. I have already done a lesson on introducing the Normal distribution and calculating probabilities from the Normal curve using the tables. I would appreciate any feedback! There were a couple of mistakes which have now been amended!

#### Discrete Random Variables Puzzle

Jigsaw puzzle on DRV that needs accompanying sheet

#### WJEC C3, C4 and S1 Revision Relay

Designed for revising modules C3, C4 and S1 from the WJEC A Level Maths specification. Inspired by the C2 Revision Relay found on www.resourceaholic.com. Creates a bit of healthy competition during revision time!Instructions: Print the Question Sheets (one per pair), laminate (optional) and cut up into separate questions. Print the Answer Sheets (one per pair).  Hand out the Answer Sheets and spare paper for workings. Hand out Question 1 to each pair. When a student brings you their Answer Sheet showing the correct answer, give them the next question. If they are incorrect, let them try again. The winning team is the first to answer Question 10 correctly.

#### Introduction to Binomial Distribution PowerPoint

Introduction to Binomial Distribution with worked examples. It starts with an opening question on discrete random variables and leads into an explanation with worked examples, followed by a couple of practice questions.

#### Stats 1 crossword

A crossword to help students revise key aspects of the OCR S1 module, made using Hot Potatoes. There are two versions - an interactive web page, and a Word document for use with good old paper and pen. If you use this resource, please take the time to review it. Any comments will be carefully noted. Topics also included: revision.

#### Team Revision Tasks - Statistics 1 (Edexcel)

These are an attempt to break from the monotony of past papers in the run up to exam season. I have taken 2 questions from past papers and put them on one sheet; I will photocopy onto A3 for students to have a go in groups and discuss. The aims/rules etc are all listed if you wish to follow them and hopefully they all make sense. I have also provided answers.

#### Normal Distribution

Normal Curve and Normal Distribution