IB Maths AI 4.12 Definitions

This page contains our IB Maths AI definitions for 4.12. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Poisson distribution'.

All Topic 4 Sub-topics 4.1: Fundamentals Of Statistics 4.2: Visualising Statistics 4.3: Distribution Properties 4.4: Introduction To Linear Statistics 4.5: Probability 4.6: Probability Distributions 4.7: Hypotheses & Tests (HL)4.8: Data collection & categorisation (HL)4.9: Advanced linear statistics (HL)4.10: Linear transformations & combinations (HL)4.11: Confidence intervals (HL)4.12: Poisson distribution (HL)4.13: Distribution tests (HL)4.14: Transition matrices

independent probability

Describes events or random variables where knowing one outcome gives no information about the other; for Poisson variables this condition allows their totals to remain Poisson.

mean

The expected value of a random variable; if $X \sim \mathrm{Poisson}(\lambda)$ , then $E(X) = \lambda$

Poisson distribution

A discrete probability model for the number of times an event happens in a fixed interval of time, length, area, or volume, assuming events occur independently at a constant average rate.

probability

Measures how likely an event is to happen, taking a value between $0$ and $1$ , where $0$ means impossible and $1$ means certain.

variance

Measures spread using the mean of squared distances from the mean, so values far from the mean have greater influence; measured in squared units and equal to the square of the standard deviation.

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