2. Data generating distributions

This week we are thinking about how a physical process (such as tossing a coin 10 times) generates a distribution of possible outcomes (frequency of getting 1 head, 2 heads, 3 heads… 10 heads).

We will look at one distribution in which the link between the physical process (coin toss) and probability distribution can be fairly directly understood, namely the binomial distriution

We will then see how a binomial process (such as tossing a coin) applied over many trials (coin tosses) gives rise to a variable (number of heads) that follows a normal distribution

Warning

This week the tutorial exercises are split into two sets with an additional page of reading in the middle. You should read through everything up to the first set of tutorial exercises ahead of the tutorial.

2.1. Tasks for this week

Conceptual material is covered in the lecture. In addition to the live lecture, you can find lecture videos on Canvas.

Please work through the guided exercises in this section (everything up to the page labelled “Tutorial Exercises 1”) in advance of the computer-based tutorial session.

To complete the guided exercises you will need to either:

• open the pages in Google Colab (simply click the Colab button on each page), or

• download them as Jupyter Notbooks to your own computer and work with them locally (eg in JupyterLab)

If you find something difficult or have questions, you can discuss with your tutor in the computer-based tutoral session.

This week is particularly heavy on conceptual material, so please do discuss the guided exercises and tutorial exercises with your tutor to make sure you understand