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Competitive
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Revision Notes
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Revision Notes
Practice Questions
Topical Past Paper Questions
Past Papers
Probability & Statistics 1
/
The binomial and geometric distributions
Contents
Binomial probabilities
Contents
All chapters
Mathematics · 9709
Probability & Statistics 1
Chapter 07 · The binomial and geometric distributions
Binomial Models
Binomial probabilities
01
Representation of Data
Data and Display Choice
2
Types of Data
Choosing a Representation
Stem-and-Leaf Diagrams
1
Stem-and-Leaf Diagrams
Histograms
1
Histograms
Cumulative Frequency
2
Constructing Cumulative-Frequency Graphs
Reading Cumulative-Frequency Graphs
02
Measures of central tendency
Modes and Means
2
Mode and the Modal Class
The Mean
Mean Totals and Coding
2
Combined Means and Changing Data
Coded Data and Totals
Median and Measure Choice
2
The Median
Choosing an Average
03
Measures of variation
Range and Quartiles
3
Why spread matters and the range
IQR and box plots
Quartiles from cumulative frequency
Standard Deviation
1
Standard deviation
Totals and Coding
2
Variance from totals and combined data
Coded data: shift and scale
04
Probability
Probability Foundations
1
Probability language and sample spaces
Event Relationships
2
OR, exclusive events and Venn diagrams
AND and independent events
Conditional Events and Trees
2
Conditional probability
Dependent events and probability trees
05
Permutations and combinations
Counting Arrangements
2
Counting choices and factorials
Arrangements in a line
Restricted and Partial Arrangements
3
Arrangements with restrictions
Digit arrangements
Arranging r from n
Selections and Counting Probability
3
Permutations or combinations?
Combination casework
Combinations in probability
06
Probability distributions
Random Variables and Distribution Tables
4
Discrete random variables
Building a distribution from outcomes
Distributions from selections and stopping rules
Completing and using a distribution
Expectation and Spread
2
Expectation of a random variable
Variance and standard deviation
07
The binomial and geometric distributions
Binomial Models
4
Recognising a binomial model
Binomial probabilities
Binomial mean and variance
Binomial complements and least n
Waiting for Successes
3
The geometric distribution
Later success on a given trial
Geometric mean and mode
08
The normal distribution
Normal Models and Probability
3
Continuous variables and normal curves
The standard normal distribution and Φ
Standardising a normal variable
Normal Models in Context
2
Using normal probabilities in context
Finding μ and σ from probabilities
Normal Approximation to the Binomial
2
When a normal approximation is suitable
Continuity correction and the complete method
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