Conquer

The AcademyWelcome back

Skip to content

ConquerYOUR A LEVELS

Subjects

CCambridge EPearson Edexcel AQAAQA OCROCR

Competitive Study space Mistake Bank AI Marking

Log in Try for free

Study space Mistake Bank AI Marking

Subjects

CCambridge EPearson Edexcel AQAAQA OCROCR

Competitive Try for free Log in Create free account

Further Mathematics · 9231

Further Probability & Statistics

01Continuous random variables

Probability density3

Understanding probability density Checking and normalising a PDF Piecewise PDFs and probabilities

Cumulative distributions3

Building a cumulative distribution Using and differentiating a CDF Medians, quartiles and percentiles

Averages and spread3

Finding the mode Mean, variance and standard deviation Expectations of functions of X

Transformed variables2

Increasing transformations Decreasing transformations and branches

Infinite ranges and review2

Distributions on infinite intervals Formula reference and mixed review

02Inferential statistics

Sampling and t distributions2

Sampling error and variance estimates The t distribution and critical values

Hypothesis tests4

Testing one population mean Independent means and pooled variance Paired sample t tests Choosing the appropriate test

Confidence intervals3

Confidence intervals for one mean Confidence intervals for differences Interval width, formula reference and review

03Chi-squared tests

Goodness of fit3

Observed counts, expected counts and discrepancy Goodness-of-fit tests Combining categories and degrees of freedom

Fitting distributions2

Fitting binomial and Poisson distributions Fitting continuous distributions

Independence2

Independence in contingency tables Formula reference and mixed review

04Non-parametric tests

Sign and rank tests3

Choosing a non-parametric test Single-sample sign tests Wilcoxon signed-rank tests

Comparing populations2

Paired sign and signed-rank tests Wilcoxon rank-sum tests

Normal approximations3

Normal approximations for signs and signed ranks Normal approximation for rank sums Formula reference and mixed review

05Probability generating functions

Constructing PGFs3

What a probability generating function represents Uniform and binomial PGFs Geometric and Poisson PGFs

Using PGFs2

Extracting probabilities from a PGF Mean, variance and unknown probabilities

Combining variables4

Sums of independent random variables Transformations and repeated observations Constructing PGFs from a process Formula reference and mixed review

Revision Notes Practice Questions Topical Past Paper Questions Past Papers

Resources

Revision Notes Practice Questions Topical Past Paper Questions Past Papers

Further Probability & Statistics/Probability generating functions

Extracting probabilities from a PGF

Choose between targeted expansion and derivatives at zero.

Practise Probability generating functions

Contents

Further Mathematics · 9231

Further Probability & Statistics

01Continuous random variables

Probability density3

Understanding probability density Checking and normalising a PDF Piecewise PDFs and probabilities

Cumulative distributions3

Building a cumulative distribution Using and differentiating a CDF Medians, quartiles and percentiles

Averages and spread3

Finding the mode Mean, variance and standard deviation Expectations of functions of X

Transformed variables2

Increasing transformations Decreasing transformations and branches

Infinite ranges and review2

Distributions on infinite intervals Formula reference and mixed review

02Inferential statistics

Sampling and t distributions2

Sampling error and variance estimates The t distribution and critical values

Hypothesis tests4

Testing one population mean Independent means and pooled variance Paired sample t tests Choosing the appropriate test

Confidence intervals3

Confidence intervals for one mean Confidence intervals for differences Interval width, formula reference and review

03Chi-squared tests

Goodness of fit3

Observed counts, expected counts and discrepancy Goodness-of-fit tests Combining categories and degrees of freedom

Fitting distributions2

Fitting binomial and Poisson distributions Fitting continuous distributions

Independence2

Independence in contingency tables Formula reference and mixed review

04Non-parametric tests

Sign and rank tests3

Choosing a non-parametric test Single-sample sign tests Wilcoxon signed-rank tests

Comparing populations2

Paired sign and signed-rank tests Wilcoxon rank-sum tests

Normal approximations3

Normal approximations for signs and signed ranks Normal approximation for rank sums Formula reference and mixed review

05Probability generating functions

Constructing PGFs3

What a probability generating function represents Uniform and binomial PGFs Geometric and Poisson PGFs

Using PGFs2

Extracting probabilities from a PGF Mean, variance and unknown probabilities

Combining variables4

Sums of independent random variables Transformations and repeated observations Constructing PGFs from a process Formula reference and mixed review

Search resources