Procedure for the experiments in the following section

In the experiment section there are 3 sub experiment which enhance the students understanding of random variables and the terms associated with it.

Sub Experiment (Sigma algebra) :

In this subexperiment there are 2 examples which help build the students understanding of sigma algebra with the help of the definition that is available in the theory section

• There is an incomplete collection of sets for which one must choose the appropriate sets (more than or equal to 1) to be added to the collection which ensures that the collection is the smallest possible sigma algebra.

• The user must select the sets from the pink tile displayed below. Once a selection has been made, a blue tile appears below which marks the anwer chosen by the user.

• Once a particular pink tile is chosen and then the user wishes to change the answer, the user can then proceed to click on the blue tile and reselect another pink tile.

• Upon selection of the required number of tiles, the user must click on the submit button to check if the selected tiles make the collection a sigma algebra.

• The user is only allowed to choose a predetermined number of minimum tiled for each individual example. (For example only 1 tile can be selected for the first example)

• In the observation section the result will be displayed.

Sub Experiment (Inverse image) :

This sub experiment helps users to build their understanding of inverse image of a random variable function.

• There is a function $\mathcal{f}: \Omega \to \mathbb{R}$ defined over a sample space $\Omega$ which has has 4 elements in it.

• The user has to input a value for $c$ for which they want to find the inverse image for, given by $f^{-1}(c)$.

• Once the user has entered the value for $c$, they have to click on the $Generate$ button to produce mappings of the elements of $\Omega$ onto $\mathbb{R}$.

• Based on the values generated by the random generator function, the user has to select the appropriate set which reflects the inverse image of $c$ of the function $\mathcal{f}$.

• Once a user selects any of the options, the result of the selection is displayed in the observation section.

• If the user has chosen a correct answer, a graph is displayed showing the mappings of the function as well as the inverse image

Sub Experiment (Valid Random Variable) :

This sub experiment helps users to build their understanding of the requirements for a function to be a valid random variable.

• There are 4 images of different function mappings displayed to the user out of which one or more might be valid random variable mapping.

• The user can choose any of the 4 images displayed.

• Once a selection has been made, the user can click on the $Submit$ button to check if their answer is correct or incorrect.

• Once the submit button has been clicked, information about that particular image and the explanation as to why the selected function mapping is a valid random variable is displayed.