S2.2 - Continuous random variables

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.