I think most people who’d benefit from reading this will bounce off the equations above. Here is a concrete example that I think is easy to understand.
Consider a variable X that can be 1 or 2 with equal probability.
E(X) = (1+2)/2 = 1.5
So 1/E(X) = 1⁄1.5 = 0.667
Whereas, E(1/X) = (1/1 + 1⁄2)/2 = 0.75
So sometimes 1/E(X) does not equal E(1/X).
I think most people who’d benefit from reading this will bounce off the equations above. Here is a concrete example that I think is easy to understand.
Consider a variable X that can be 1 or 2 with equal probability.
E(X) = (1+2)/2 = 1.5
So 1/E(X) = 1⁄1.5 = 0.667
Whereas, E(1/X) = (1/1 + 1⁄2)/2 = 0.75
So sometimes 1/E(X) does not equal E(1/X).