[math] Empirical distribution function

 

Example:

Let's look at a real example with 5 marbles of different sizes. Imagine their sizes are 1, 2, 2, 3, 5

Here is what our "marble staircase" looks like:

How to read your stairs:

1. The Bottom (Ground): We start at 0 because we haven't seen any marbles yet.

2. Size 1: Find first marble! We take a step up. Now we've seen1/5 (or 20%) of the marbles.

3. Size 2: Find two marbles that are the same size! This makes a double step up. Now we've seen 3/5 (or 60%) of the marbles.

4. Size 3: Another marble! Another step up to 4/5 (or 80%).

5. Size 5: The last, biggest marble! One final step takes you to the very top 100%.