Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 43 / 5 / i

For $0\le s\le 1$, pointwise concavity of the utility function givesTaking expectations is legitimate because all three values are finite. Therefore $\boxed{F(s\theta +(1-s)\eta )\ge sF(\theta )+(1-s)F(\eta )}$: $F$ is concave. Strict concavity is not required and is not asserted.