is unlikely to be suitable. Recognise situations in which both the Poisson In a situation where the binomial model is Formal criteria. R12 distribution and the binomial distribution might be appropriate, if is large and is small, then the Using the Poisson appropriate models. conditions for a Poisson distribution to be distribution as a appropriate are approximately satisfied. In the numerical absence of guidance either model can be approximation for used. calculating binomial probabilities. Be able to calculate probabilities using a Poisson Including use of a calculator to access R13 distribution. Poisson probabilities and cumulative Poisson probabilities. Know and be able to use the mean and variance of a Proof. R14 Poisson distribution. Know that the sum of two or more independent and Proof. R15 Poisson distributions is also a Poisson distribution. when and are independent. Ref. Learning outcomes Exclusions Notes Notation Specification The geometric Recognise situations under which the geometric Link with corresponding binomial distribution. , wherenumber of SR16 The alternative distribution distribution is likely to be an appropriate model. Bernoulli trials up to and definition which including the first counts the success. number of failures. Be able to calculate the probabilities within a where R17 geometric distribution, including cumulative probability of success and . probabilities. . An understanding of the calculation is expected. Be able to use the mean and variance of a geometric . R18 Proof. distribution.
is unlikely to be suitable. R12 Recognise situations in which both the Poisson distribution and the binomial distribution might be appropriate models. In a situation where the binomial model is appropriate, if is large and is small, then the conditions for a Poisson distribution to be appropriate are approximately satisfied. In the absence of guidance either model can be used. Formal criteria. Using the Poisson distribution as a numerical approximation for calculating binomial probabilities. R13 Be able to calculate probabilities using a Poisson distribution. Including use of a calculator to access Poisson probabilities and cumulative Poisson probabilities. R14 Know and be able to use the mean and variance of a Poisson distribution. Proof. R15 Know that the sum of two or more independent Poisson distributions is also a Poisson distribution. and when and are independent. Proof. Specification Ref. Learning outcomes Notes Notation Exclusions The geometric distribution SR16 Recognise situations under which the geometric distribution is likely to be an appropriate model. Link with corresponding binomial distribution. , wherenumber of Bernoulli trials up to and including the first success. The alternative definition which counts the number of failures. R17 Be able to calculate the probabilities within a geometric distribution, including cumulative probabilities. where probability of success and . . An understanding of the calculation is expected. R18 Be able to use the mean and variance of a geometric distribution. . Proof.
461318-further-statistics-discrete-random-variables-delivery-guide-version-1-.docx