In this video, the professor 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.

In this video, 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.