I don’t like the notation Varrem[Y|X] because X appears as a free RV but actually it’s averaged over. I think it would be better to write E[Var[Y|X]].
The notation in the post is inspired by similar notation for conditional entropy:
Conventionally Var[Y|X] is a random variable, just like how E[Y|X] is a random variable. To be fair the conventions are somewhat inconsistent, given that (as you said) H(Y|X) is a number.
Okay, you people convinced me to change the notation!
Yeah I had complaints when I was taught that formula as well!
I don’t like the notation Varrem[Y|X] because X appears as a free RV but actually it’s averaged over. I think it would be better to write E[Var[Y|X]].
The notation in the post is inspired by similar notation for conditional entropy:
Conventionally Var[Y|X] is a random variable, just like how E[Y|X] is a random variable. To be fair the conventions are somewhat inconsistent, given that (as you said) H(Y|X) is a number.
Okay, you people convinced me to change the notation!
Yeah I had complaints when I was taught that formula as well!