Suppose that .S; P1/ and .S; P2/ are two sample spaces that have the same set of outcomes, S. Is it possible that each outcome is less likely in the first sample space than it is in the second? That is, can we have 8s 2 S; P1.s/ < P2.s/?

Lecture 23: Extreme Values (Section 4.2) Def. Af uncin f has an absolute maximum at x = c if f(x)=2 −| x| 4 3 2 1 0 −4 −3 −2 −1 0 1 2 3 4 −1 −2 −3 −4 f(c)s ithe of f on D. Def. f has an absolute minimum at x = c if 2 f(x)= x − 1 4 3