1 f(x) = = 1 {0.2 ≤ x ≤ 1} 5x Here's the game. At the start you choose your level of risk x―it could be anywhere between 0.2 and 1. Following that, a random number z is generated between 0 and 1. If z is greater than or equal to x, you win, and receive a payoff of f(x). If z is less than x, you lose, and receive a payoff of 0. (a) Use calculus to find the value of x that maximizes your average payoff. -0.8 -0.6 -0:4 -0.2 0.2 0.4 0.6 0.8

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