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Unit S2: Statistics 2

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4 topics · 16 learning objectives

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  1. S2.1 - The Binomial and Poisson distributions

    1. S2.1.1Binomial and Poisson distributions

      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).

    2. S2.1.2Mean and variance of binomial and Poisson distributions

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

    3. S2.1.3The

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

  2. S2.2 - Continuous random variables

    1. The concept of a continuous random variable.

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

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

    4. Mean and variance of continuous random variables.

    5. Mode, median and quartiles of continuous random variables.

  3. S2.3 - Continuous distributions

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

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

  4. S2.4 - Hypothesis tests

    1. 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.

    2. Concepts of a statistic and its sampling distribution.

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

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

    5. One-tailed and two-tailed tests.

    6. 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.