Probability Models

This lesson covers the use of probability distributions — particularly the binomial and normal distributions — as models for real-world data. You will learn how to select an appropriate model, check its suitability, and compare model predictions with observed data from the large data set.

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What Is a Probability Model?

A probability model is a mathematical description of a random process. It specifies the possible outcomes and the probability of each outcome. In A-Level Mathematics, the two most important probability models are:

1. Binomial distribution — for counting the number of successes in a fixed number of independent trials.
2. Normal distribution — for modelling continuous data that is symmetrically distributed around the mean.

The key idea is that we use these mathematical models to approximate real-world situations. No model is a perfect representation of reality, but a good model captures the essential features of the data and allows us to make useful predictions.

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The Binomial Distribution as a Model

Conditions for the Binomial Model

The random variable $X$X follows a binomial distribution $X \sim B(n, p)$X∼B(n,p) if: