Why use beta distribution here and why it is beta(1,2)

rden ex Exercise 5.1 Consider a single-item auction with two bidders with valuations drawn independently from the uniform distribution on 10, 1). In what follows let Vin = min ( VijV=) que Voi = max (V,, V2) so Ving = (2) (a) Prove that the expected revenue obtained by a second-price auction (with no reserve) is 5. Facts Vig~ Beta ( 1, 2) E ( V () ) = xf (t)d x with density flv )= 2(1-v) = 2 x(1-xldt 1/3 E ( Beta ( v , 5 )) = FAS oh average Su E (Bete (1,2) ) = 3