3.4.1 SA: Discrete random variables (DRVs) and expectation
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SA1
Understand DRVs with distributions given in the form of a table or function.
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SA2
Evaluate probabilities for a DRV.
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SA3
Evaluate measures of average and spread for a DRV to include mean, variance, standard deviation, mode and median.
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SA4
Understand expectation and know the formulae:;;
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SA5
Understand expectation of linear functions of DRVs and know the formulae:
and
Know the formula
Find the mean, variance and standard deviation for functions of a DRV such as
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SA6
Know the discrete uniform distribution defined on the set . Understand when this distribution can be used as a model.
3.4.2 SB: Poisson distribution
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SB1
Understand conditions for a Poisson distribution to model a situation. Understand terminology .
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SB2
Know the Poisson formula and calculate Poisson probabilities using the formula or equivalent calculator function.
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SB3
Know mean, variance and standard deviation of a Poisson distribution.
Use the result that, if then the mean and variance of are equal.
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SB4
Understand the distribution of the sum of independent Poisson distributions.
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SB5
Formulate hypotheses and carry out a hypothesis test of a population mean from a single observation from a Poisson distribution using direct evaluation of Poisson probabilities.
3.4.3 SC: Type I and Type II errors
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SC1
Understand Type and Type errors and define in context. Calculate the probability of making a Type error from tests based on a Poisson or Binomial distribution.
Calculate probability of making Type error from tests based on a normal distribution.
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SC2
Understand the power of a test. Calculations of P(Type error) and power for a test for tests based on a normal, Binomial or a Poisson distribution.
3.4.4 SD: Continuous random variables (CRVs)
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SD1
Understand and use a probability density function,, for a continuous distribution and understand the differences between discrete and continuous distributions.Understand and use distributions of random variables that are part discrete and part continuous.
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SD2
Find the probability of an observation lying in a specified interval.
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SD3
Find the median and quartiles for a given probability density function,.
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SD4
Find the mean, variance and standard deviation for a given pdf, . Know the formulae
, ,
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SD5
Understand the expectation and variance of linear functions of CRVs and know the formulae:
and
Know the formula
Find the mean, variance and standard deviation of functions of a continuous random variable such as
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SD6
Understand and use a cumulative distribution function, . Know the relationship between and .
and
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SD8
Know that if and are independent (discrete or continuous) random variables then and
3.4.5 SE: Chi squared tests for association
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SE1
Construction ofcontingency tables.
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SE2
Use of as an approximate statistic with appropriate degrees of freedom.
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SE3
Know and use the convention that allshould be greater than 5.
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SE4
Identification of sources of association in the context of a question.
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SE5
Knowledge of when and how to apply Yates’ correction.
3.4.6 SF: Exponential distribution
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SF1
Know the conditions for an exponential distribution to be used as a model. Know the probability density function,, and the cumulative distribution function,, for an exponential distribution.
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SF2
Calculate probabilities for an exponential distribution usingor integration of
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SF3
Know proofs of mean, variance and standard deviation for an exponential distribution.
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SF4
Understand that the lengths of intervals between Poisson events have an exponential distribution.
3.4.7 SG: Inference – one sample t- distribution
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SG1
Test for the mean of a normal distribution with unknown variance using a
with appropriate degrees of freedom.
3.4.8 SH: Confidence Intervals
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SH1
Construct symmetric confidence intervals for the mean of a normal distribution with known variance.
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SH2
Construct symmetric confidence intervals from large samples, for the mean of a normal distribution with unknown variance.
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SH3
Make inferences from constructed or given confidence intervals.
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SH4
Construct symmetric confidence intervals from small samples, for the mean of a normal distribution with unknown variance using the-distribution.