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-MATHEMATICS TEACHER-
Mr Valmonte's Maths Page

A-Level Specifications
Textbook



Further Statistics 1 OBJECTIVES
Discrete Random Variables
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Find the expected value of a discrete random variable X
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Find the expected value of X^2
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Find the variance of a discrete random variable
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Use the expected value and variance of a function X
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Solve problems involving random variables
Poisson Distribution
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Use the Poisson distribution to model real-world situations
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Use the additive property of the Poisson distribution
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Understand and use the mean and variance of the Poisson distribution
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Understand and use the mean and variance of the binomial distribution
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Use the Poisson distribution as an approximation to the binomial distribution
Geometric and Negative Binomial Distribution
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Understand and use the geometric distribution
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Calculate and use the mean and variance of the geometric distribution
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Understand and use the negative binomial distribution
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Calculate and use the mean and variance of the negative binomial distribution
Hypothesis Testing
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Use hypothesis tests to test for the mean of a Poisson distribution
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Find critical regions of a Poisson distribution using tables
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Use hypothesis tests to test for the parameter p in a geometric distribution
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Find critical regions of a geometric distribution
Central Limit Theorem
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Understand and apply the central limit theorem to approximate the sample mean of a random variable, X
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Apply the central limit theorem to other distributions
Chi-Squared Tests
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Form hypothesis about how well a distribution fits as a model for an observed frequency distribution and measure goodness of fit of a model to observed data
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Understand degrees of freedom and use the chi-squared (X^2) family of distributions
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Be able to test a hypothesis
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Apply goodness-of-fit tests to discrete data
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Use contingency tables
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Apply goodness-of-fit tests to geometric distributions
Probability Generating Functions
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Understand the use of probability generating functions
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Use probability generating functions for standard distributions
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Use probability generating functions to find the mean and variance distribution
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Know the probability generating function of the sum of independent random variables
Quality of Tests
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know about Type I and Type II errors
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Find Type I and Type II errors using the normal distribution
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Calculate the size and power of a test
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Draw a graph of the power function for a test
Further Statistics 2 OBJECTIVES
Linear Regression
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Calculate the equation of a regression line using raw data or summary statistics
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Use coding to find the equation of a regression line
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Calculate residuals and use them to test for linear fit and identify outliers
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Calculate re residual sum of squares (RSS)
Correlation
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Calculate the value of the product moment correlation coefficient
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Understand the effect of coding on it and understand the conditions for its use
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Calculate and interpret Spearman's rank correlation coefficient
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Carry out hypothesis tests for zero correlation using either Spearman correlation coefficient rank or the product moment correlation coefficient
Continuous Distributions
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Understand and use the probability density function for a continuous random variable
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Understand and use the cumulative distribution function for continuous random variable
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Find the mean, variance, mode, median and percentiles of a continuous random variable and describe the skewness
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Understand, use and model situations using the continuous uniform distribution
Combinations of Random Variables
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Find the distribution of linear combinations of normal random variables
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Solve modelling problems involving combinations of normal random variables
Estimation, Confidence Intervals and Tests using a Normal Distribution
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Understand and use estimates and estimators
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Undestand bias
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Find the standard error
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Calculate and use confidence intervals for population parameters
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Carry out hypothesis tests for the difference between the means of two normally distributed random variables with known variances
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Carry out hypothesis tests using large sample results in cases where the population variance is unknown
Further Hypothesis Tests
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Find a confidence interval for the variance of a normal distribution
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Conduct a hypothesis test for the variance of a normal distribution
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Understand and use the F-distribution
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Carry out na F-test to test whether two independent random variables are from normal distributions with equal variances
Confidence Intervals and Tests using the t-distribution
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Find a confidence interval for the mean of a normal with unknown variance
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Conduct a hypothesis test for the mean of a normal distribution with unknown variance
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Carry out a paired t-test
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Find a confidence interval for the difference between two means from independent normal distributions with equal but unknown variances
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Conduct a hypothesis test for the difference between two means from independent normal distributions with equal but unknown variances
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