Consider an EU maximizer with utility function u(x) = x ; 0 < 1. (a) Find a certainty equivalent of a r.v.

Consider an EU maximizer with utility function u(x) = x^α; 0 ≤ α < 1. 

(a) Find a certainty equivalent of a r.v. X₁ =b>0 or 0 with respective probabilities p and q=1−p. 

(b) Compare it with the certainty equivalent of a r.v. X₂ uniform on [0,b].

Which certainty equivalent is larger for p = 1/2? (The means are the same.) Interpret the answer.