Random Variables

Procedure for the experiments in the following section

In the experiment section there are 3 sub-experiment, which are the following experiments

• Sigma algebra
• Inverse image
• Valid random variable

Sub-Experiment 1 ($\sigma$ algebra) :

In this sub-experiment, there are a few examples, one of which is selected randomly:

• For each example, select the required sets from the pink tiles to form the smallest $\sigma$ algebra.
• Selected tiles turn blue; click a blue tile to change your selection.
• Click Submit to check your answer.
• The minimum number of tiles to select is specified for each example.
• Results are shown in the observation section.

Sub-Experiment 2 (Inverse image) :

This sub-experiment helps users understand the inverse image of a random variable function.

• Users first need to input a value for $c$.
• We then generate random function values for $\mathcal{f}: \Omega \to \mathbb{R}$
• Users select the subset of $\Omega$ that corresponds to the inverse image $f^{-1}(c)$ from the given options.
• Results are shown in the observation box once users press Submit button.

Sub-Experiment 3 (Valid random variable) :

In this sub-experiment, there are a few examples, one of which is selected randomly:

• 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.