S2.3 - Continuous distributions

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.