Provide an opening paragraph or two that motivates the problem by describing why the topic is useful. It could be that the tool itself is immediately useful in some applications or that the tool is used to build towards more complex methods that are useful in some applications. The nice thing about statistics is that somewhere down the line, it is all about the application. You should identify the application of your topic in the first paragraph or two.
A final paragraph of the introduction should tell your reader the structure of your tutorial. You should tell them that you will next offer a section that show cases a specific example of the topic, then the general mathematics behind the topic, another specific example, and last a conclusion.
You should then provide a specific example of the topic you are writing about. You will most likely need to walk the reader through your example in plain and simple language, giving a more intuitive feel for the topic.
This section will provide the more general mathematics behind the topic. Use the opening specific example to provide grounding to the more abstract mathematical topics.
(A Different) Specific Example
This section should provide a more in-depth specific example. This next example should help your audience see more deeply into the topic at hand. On the one hand, you can think of this as just a more complex example. On the other hand, maybe your example is not more complex so much as it helps see something not so obvious about the general mathematics.
Tell your audience what you just told them and remind them why this is important.
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