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!
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!