[adrianN]

If heads is 1 and tails is 0 then the expected value is 0.5. The expectation really depends on what values your random variable can take.

[EricBurnett]

That's not the non convex case though (as e.g. 1 and -1 is). You're right that chance can be convex; the premise of the article is that that's the property of interest, and that randomness alone isn't sufficient.