Can you please help me understand how is the curve shrinking when we multiply x and it expands when x is divided. I was expecting the curve to expand in multiplication and vice versa in the Transformation example in the lecture “Standardising Normal Distribution”.
Thanks for reaching out!
We’ve been going back and forth with this since some students like the notation and some don’t because most get that it’s just mapping, while others think we’re transforming the function rather than the data set. In short, it should be expanding when multiplying and shrinking when dividing since we’re taking every element of the dataset and multiplying/dividing it by a given number (which is exactly how you perceived it).
This is what we had initially and some students argued that it should be the other way around because that’s how function transformations work, so eventually (against our better judgement) we changed it to adhere to those students. Right now it’s a bit of a hot mess and we’re thinking of the easiest ways to change the lecture to make everything both accurate and simple enough.
In short, you are right, it should be multiply -> expand and divide -> shrink and we’re currently contemplating how to rework the entire lecture to help other students grasp the concept the exact same way you did.
Sorry for confusing you!