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

The Normal distribution,

the Student-T distribution, and

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.