0.For which lotteries with random outcomes X is the above function a utilityfunction? Explain your answer and give an example of a lottery or specify a distibutionof the random variable X for which...

Extracted text: . Explain the interpretation of a utility function and why such a function should be increasing. is said that the utility function of a decision maker is given by Ua(x) = 2ax – x², r € R for some a > 0.For which lotteries with random outcomes X is the above function a utility function? Explain your answer and give an example of a lottery or specify a distibution of the random variable X for which the function mentioned in relation 2 is not a utility function. 3. Consider a decision maker with initial wealth 0 and this decision maker needs to play a lottery L having a random outcome X bounded above by a > 0. This means P(X < a)="1." is="" this="" decision="" maker="" risk="" averse="" or="" risk="" seeking="" for="" this="" particular="" lottery?="" explain="" your="" answer="" and="" give="" the="" definion="" of="" riskaverse="" and="" risk="" seeking!="" 4.="" let="" a=""> 0 be given and L a lotery with random outcome X having cumulative distribution function if r < 0="" f(x)="{" a-lx="" if="" 0="">< x="">< a="" if="" r=""> a and assume that the utility function of the decision maker having initial wealth w = 0 is given by the function uq listed in relation 2. Compute the expected utility of this lottery and the certainty equivalence of this lottery.