Missing explanation - Joint distribution - continuous

In the lecture on continuous joint probabilty the example is given of call center wait times vs customer rating. The data is initially depicted as a scatter plot, and then a heatmap - the heatmap being generated by binning the data I am guessing. So far so good.

From there though a 3D graph of the joint probability density is shown which appears to be continuous for joint probability (i.e. is a combined PDF for both distributions) however there is no explanation for how this is generated which is the whole point of the lecture - how is a continuous PDF for two variables actually produced, how are the probalities for the graph generated? It does not explain in the lecture and in the following lecture the graph is then used again for extracting the marginal distribution but it is not explained what function is being used to generate the PDF in the first place.

Is it possible a slide or video is missing as it seems quite crucial for this section?

I’m sorry for asking another question but I am really trying to understand this topic.

Hi, thanks for your feedback.

So far it is not missing. The idea for a PDF remains the same: for the values in its domain, the PDF returns the “likelihood” of that value to occur (remember that single points in continuous distributions have probability zero). So the PDF for this case would be a function f(x,y) such that x = \text{waiting time} and y = \text{customer rating} and the value f(x,y), in this case, would be the normalized amount of points in each cluster.

I agree that we should go a bit slower in this video. I will open an issue regarding this to maybe add a few slides and explain how the 3D graph is being calculated.