Unit S2: Statistics 2

The binomial and Poisson Students will be expected to use these distributions to distributions. model a real-world situation and to comment critically on their appropriateness.; Cumulative probabilities by calculation or by reference to tables.; Students will be expected to use the additive property of the Poisson distribution – e.g. if the number of events per minute ∼ Po(λ) then the number of events per 5 minutes ∼ Po(5λ).

Use binomial and poisson distributions to connect the rule to the data and decision in the question.

This matters because binomial and poisson distributions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply binomial and poisson distributions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Binomial and Poisson distributions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The mean and variance of the No derivations will be required. binomial and Poisson distributions.

Use mean and variance of binomial and poisson distributions to connect the rule to the data and decision in the question.

This matters because mean and variance of binomial and poisson distributions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply mean and variance of binomial and poisson distributions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Mean and variance of binomial and Poisson distributions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The use of the Poisson distribution as an approximation to the binomial distribution.

Use the to connect the rule to the data and decision in the question.

This matters because the determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply the to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: The is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The concept of a continuous random variable.

Use concept of a continuous random variable to connect the rule to the data and decision in the question.

This matters because concept of a continuous random variable determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply concept of a continuous random variable to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: concept of a continuous random variable is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use a probability density f(x) and cumulative distribution F(x0) = P(X ≤ x0) = ∫_{−∞}^{x0} f(x) dx, including simple piecewise polynomial densities.

Use probability density and cumulative distribution functions to connect the rule to the data and decision in the question.

This matters because probability density and cumulative distribution functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply probability density and cumulative distribution functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Probability density and cumulative distribution functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Relationship between density and dF(x) f(x) =. distribution functions. dx.

Use relationship between density and df(x) f(x) = to connect the rule to the data and decision in the question.

This matters because relationship between density and df(x) f(x) = determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply relationship between density and df(x) f(x) = to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Relationship between density and dF(x) f(x) = is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Mean and variance of continuous random variables.

Use mean and variance of continuous random variables to connect the rule to the data and decision in the question.

This matters because mean and variance of continuous random variables determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply mean and variance of continuous random variables to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Mean and variance of continuous random variables is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Mode, median and quartiles of continuous random variables.

Use mode, median and quartiles of continuous random variables to connect the rule to the data and decision in the question.

This matters because mode, median and quartiles of continuous random variables determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply mode, median and quartiles of continuous random variables to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Mode, median and quartiles of continuous random variables is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The continuous uniform Including the derivation of the mean, variance and (rectangular) distribution. cumulative distribution function.

Use continuous uniform to connect the rule to the data and decision in the question.

This matters because continuous uniform determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply continuous uniform to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: continuous uniform is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use of the Normal distribution as an approximation to the binomial distribution and the Poisson distribution, with the application of the continuity correction.

Use normal approximation to the binomial distribution to connect the rule to the data and decision in the question.

This matters because normal approximation to the binomial distribution determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply normal approximation to the binomial distribution to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Normal approximation to the binomial distribution is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Population, census and sample.; Students will be expected to know the advantages and Sampling unit, sampling frame. disadvantages associated with a census and a sample survey.

Use population, census and sample to connect the rule to the data and decision in the question.

This matters because population, census and sample determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply population, census and sample to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Population, census and sample is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Concepts of a statistic and its sampling distribution.

Use concepts of a statistic and its sampling distribution to connect the rule to the data and decision in the question.

This matters because concepts of a statistic and its sampling distribution determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply concepts of a statistic and its sampling distribution to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Concepts of a statistic and its sampling distribution is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Concept and interpretation of a Use of hypothesis tests for refinement of mathematical hypothesis test.; Null and alternative models. hypotheses.

Use concept and interpretation to connect the rule to the data and decision in the question.

This matters because concept and interpretation determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply concept and interpretation to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Concept and interpretation is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Critical region.; Use of a statistic as a test statistic.

Use critical region to connect the rule to the data and decision in the question.

This matters because critical region determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply critical region to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Critical region is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

One-tailed and two-tailed tests.

Use one-tailed and two-tailed tests to connect the rule to the data and decision in the question.

This matters because one-tailed and two-tailed tests determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply one-tailed and two-tailed tests to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: One-tailed and two-tailed tests is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Hypothesis tests for the parameter p Students are expected to know how to use tables to carry of a binomial distribution and for out these tests.; Questions may also be set not involving the mean of a Poisson distribution. tabular values.; Tests for the parameter p of a binomial distribution may involve the use of a normal approximation to calculate probabilities.

Use hypothesis tests for the parameter p to connect the rule to the data and decision in the question.

This matters because hypothesis tests for the parameter p determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply hypothesis tests for the parameter p to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Hypothesis tests for the parameter p is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.