In this [video][1], Blitzstein says that some random variables have no pdf but do have a cdf. Also, in my course material, I studied that converging in mean was stronger than converging in cdf which itself was stronger than converging in pdf.

I understand the maths behind it but I cannot think of an intuitive explanation for this. 


  [1]: https://youtu.be/OprNqnHsVIA?t=1145