IB Maths AI 4.6 Notes

This page contains our IB Maths AI notes for 4.6. By reading each one of these notes, you will fully cover the content for IB Maths AI 'Probability distributions'.

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

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Chapters

1. Discrete random variables

2. Expected value E(X)

3. Binomial distribution

4. Normal distribution & standardization

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Discrete random variables

A random variable is a variable whose value depends on the outcome of a chance process. In this section, the focus is on discrete random variables, their probability distributions, expected value, the binomial distribution, and standardization of normal variables using $z$ -values.

A discrete random variable can take a finite or countable set of values. For example, if a fair die is rolled and $X$ is the score obtained, then $X$ can take the values $1,2,3,4,5,6$ .

A probability distribution lists all possible values of the random variable together with their probabilities.

For a valid probability distribution:

each probability must be between $0$ and $1$
the probabilities must add to $1$

Check that the following probability distribution is valid.
$x$ $1$ $2$ $3$ $4$ $5$
$P(X=x)$ $0.1$ $0.2$ $0.15$ $0.05$ $0.5$
Check that it is valid: $0.1+0.2+0.15+0.05+0.5=1$
So, the distribution is valid.

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