.A risk-averse poker player has just bet an amount of money s = 1 in a poker game. He is unsure whether the other players in the game are inexperienced or experienced, but he believes that the former has a probability pe (0,1) and the latter has a probability 1- p. Before starting the poker game, he can choose to allocate his unit time into two strategies: playing safe (S) or bluffing (B) without learning about the experience of other players. Denote the time he plays safe by a E [0,1] and the time he bluffs by 1 a. The probability of monetary outcomes from the game depends on the time he plays safe and bluffs as follows: If the other players in the game are inexperienced, he either gets a proportional return on his bet by r e (0,1/2) with probability a1/2/K, a proportional return 2r with probability (1 – a)/2/K, or loses all his money with the remaining probability (K > - a1/2 + (1 – a)1/2 for all a e [0,1]). If the other players in the game are experienced, he either gets a proportional return on his bet by -r with probability a/2/K, a proportional return -2r with probability (1 – a)/2/K, or loses all his money with the remaining probability (K > a/2 + (1 – a)1/2 for all a e [0,1]). The poker player's preferences over the monetary outcomes are represented by the Bernoullian utility function u (s) = s!/2. (i) Formulate the expected utility function of this player over the poker game. Explain your formulation.