S1.5 - Discrete random variables

The concept of a discrete random variable.

Use concept of a discrete random variable to connect the rule to the data and decision in the question.

This matters because concept of a discrete 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 discrete random variable to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: concept of a discrete random variable is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use the probability function p(x) = P(X = x) and cumulative distribution function F(x0) = P(X ≤ x0) for a discrete random variable.

Use probability and cumulative distribution functions to connect the rule to the data and decision in the question.

This matters because probability 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 and cumulative distribution functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Probability and cumulative distribution functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Mean and variance of a discrete Use of E(X), E(X 2) for calculating the variance of X. random variable.; Knowledge and use of E(aX + b) = aE(X) + b, Var(aX + b) = a2 Var(X).

Use mean and variance of a discrete to connect the rule to the data and decision in the question.

This matters because mean and variance of a discrete 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 a discrete to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Mean and variance of a discrete is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The discrete uniform distribution.; The mean and variance of this distribution.

Use discrete uniform distribution to connect the rule to the data and decision in the question.

This matters because discrete uniform distribution determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply discrete uniform distribution to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: discrete uniform distribution is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.