1. 3
  1.  

  2. 2

    I’m covered in kids so it’s hard to check, but does this not follow more quickly from Cauchy-Schwarz applied to the second given inequality?

    Edit: No, we only get a weaker result.

    1. 1

      Nice. BTW, it looks like your method could be generalized to bound avg(f^2) whenever we know avg(f) and avg(xf).