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Further Mathematics
Revision Notes
Further Probability & Statistics
Further Mathematics · Cambridge 9231
Further Probability & Statistics
5 chapters · 46 lessons
Collection
Further Pure Mathematics 1
Further Pure Mathematics 2
Further Mechanics
Further Probability & Statistics
Expand all
01
Continuous random variables
13 lessons · 5 topic areas
01
Probability density
3 lessons
Understanding probability density
Checking and normalising a PDF
Piecewise PDFs and probabilities
02
Cumulative distributions
3 lessons
Building a cumulative distribution
Using and differentiating a CDF
Medians, quartiles and percentiles
03
Averages and spread
3 lessons
Finding the mode
Mean, variance and standard deviation
Expectations of functions of X
04
Transformed variables
2 lessons
Increasing transformations
Decreasing transformations and branches
05
Infinite ranges and review
2 lessons
Distributions on infinite intervals
Formula reference and mixed review
Practise this chapter
02
Inferential statistics
9 lessons · 3 topic areas
01
Sampling and t distributions
2 lessons
Sampling error and variance estimates
The t distribution and critical values
02
Hypothesis tests
4 lessons
Testing one population mean
Independent means and pooled variance
Paired sample t tests
Choosing the appropriate test
03
Confidence intervals
3 lessons
Confidence intervals for one mean
Confidence intervals for differences
Interval width, formula reference and review
03
Chi-squared tests
7 lessons · 3 topic areas
01
Goodness of fit
3 lessons
Observed counts, expected counts and discrepancy
Goodness-of-fit tests
Combining categories and degrees of freedom
02
Fitting distributions
2 lessons
Fitting binomial and Poisson distributions
Fitting continuous distributions
03
Independence
2 lessons
Independence in contingency tables
Formula reference and mixed review
Practise this chapter
04
Non-parametric tests
8 lessons · 3 topic areas
01
Sign and rank tests
3 lessons
Choosing a non-parametric test
Single-sample sign tests
Wilcoxon signed-rank tests
02
Comparing populations
2 lessons
Paired sign and signed-rank tests
Wilcoxon rank-sum tests
03
Normal approximations
3 lessons
Normal approximations for signs and signed ranks
Normal approximation for rank sums
Formula reference and mixed review
Practise this chapter
05
Probability generating functions
9 lessons · 3 topic areas
01
Constructing PGFs
3 lessons
What a probability generating function represents
Uniform and binomial PGFs
Geometric and Poisson PGFs
02
Using PGFs
2 lessons
Extracting probabilities from a PGF
Mean, variance and unknown probabilities
03
Combining variables
4 lessons
Sums of independent random variables
Transformations and repeated observations
Constructing PGFs from a process
Formula reference and mixed review
Practise this chapter
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Further Mathematics
AS & A Level · 9231
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