QuestionQuestionConceptConceptDocumentDocument

Unit S2: Statistics 2

Start with Concept to understand a topic, then use Question Bank to check what you know.

4 topics · 16 learning objectives

Your progress

Sign in to see your mastery and mistakes.

  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. S2.2.1concept of a continuous random variable

      The concept of a continuous random variable.

    2. S2.2.2Probability density and cumulative distribution functions

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

    3. S2.2.3Relationship between density and dF(x) f(x) =

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

    4. S2.2.4Mean and variance of continuous random variables

      Mean and variance of continuous random variables.

    5. S2.2.5Mode, median and quartiles of continuous random variables

      Mode, median and quartiles of continuous random variables.

  3. S2.3 - Continuous distributions

    1. S2.3.1continuous uniform

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

    2. S2.3.2Normal approximation to the binomial distribution

      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. S2.4.1Population, census and sample

      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. S2.4.2Concepts of a statistic and its sampling distribution

      Concepts of a statistic and its sampling distribution.

    3. S2.4.3Concept and interpretation

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

    4. S2.4.4Critical region

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

    5. S2.4.5One-tailed and two-tailed tests

      One-tailed and two-tailed tests.

    6. S2.4.6Hypothesis tests for the parameter p

      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.