# Question: show that a von neumannmorgenstern utility function u is linear...

###### Question details

Show that a von Neumann-Morgenstern utility function *U*
is linear in the probabilities, i.e.,

U(αp+(1−α)p′)=αU(p)+(1−α)U(p′)for any p,p′∈Pandα∈[0,1].

Remark: We used this linear property to prove that the
indifferent curves of a preference relation which admits an
expected utility representation *U* are parallel lines.

PLEASE HELP SHOW WORK PLEASE!!