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How can I work with (parameterised) distributions in exercises?
How can I work with (parameterised) distributions in exercises?
You can define a distribution in parameters, but what can you do with this? This article explains this parameter type with a short example Written by Eric Bouwers
Updated over a week ago

Since December 2021 it is possible to define a parameter which represents a distribution. Three different distributions are currently supported:

These three distributions can be used in other parameter types to calculate the outcome of the cumulative distribution function or the probability density function for a given value. In addition, the value for a given quantile can be calculated.

But how could you use this in your exercises? In this article we explain how this can be done!

# The exercise

As an example, we will work with the following question:

Naturally, you can simply define this question with hard-coded values. However, in this case we have randomised the value for which the probability needs to be determined:

# The parameters

So how did we set up the parameters for this exercise? Let's take a look at the definitions:

First, we define a parameter `c` which takes a random value between `0.80` and `0.95`. Naturally, this range can be extended to create more possibilities. Then, we create a `Normal` distribution with standard values for mean and the standard deviation. Note that the mean and / or the standard deviation could also have been randomised.

We use this distribution to calculate the `probability` of the value being less can `c` using the cumulative distribution function. Lastly, we round the `probability` to four digits to ensure that students can look up the correct value.

# Possibilities

As mentioned above, we can add more variance to the exercise by, for example, taking a greater range for `c` or randomising the mean and standard deviation of the normal distribution.

In addition, we can also choose a different distribution such as the `Student-T` distribution, possibly with a randomised degree of freedoms.

# Questions?

Hopefully this example inspires you to create more exercises with parameterised distributions. If you want to know what else you can randomise using parameters you can find a list of all possibilities in this help article.