IB Maths AA 4.8 Definitions

This page contains our IB Maths AA definitions for 4.8. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Advanced distribution properties'.

All Topic 4 Sub-topics 4.1: Fundamentals Of Statistics 4.2: Visualising Statistics 4.3: Distribution Properties 4.4: Linear Statistics 4.5: Probability 4.6: Probability Distributions (HL)4.7: Bayes theorem (HL)4.8: Advanced distribution properties

continuous

Able to take any value within an interval.

discrete

Taking separate, countable values, usually whole numbers.

mean

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

median

The value

m

such that

\int_{-\infty}^{m} f(x)\,dx=\frac{1}{2}

, so half the total area under the density curve lies on each side.

mode

The value of

x

where the probability density function has its greatest value.

probability

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

probability density function

A function

f(x)

used to describe a continuous random variable, where

f(x)\geq0

and

\int_{-\infty}^{\infty} f(x)\,dx=1

, so probabilities correspond to areas under its graph.

standard deviation

The square root of the variance,

\sigma=\sqrt{\mathrm{Var}(X)}

, giving spread in the same units as the random variable.

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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