finance question

Assume an investor's preferences can be described by a utility function which can be expressed in terms of wealth as UIW) = 20W.5W2. The investor is considering 3 investments with the following uncertain future outcomes and probabilities of occurrence i. 1/3 chance of 6, 1/3 chance of 7 and 1/3 chance of8 ii. 1/4 chance of 4, 1/2 chance of 7 a nd 1/4 chance of 10 iii. 1/5 chance of 1, 3/5 chance of 6 and 1/5 chance of 16 1. Is this a \"well-behaved" utility function? Explain why or why not.....4 marks 2. What is the expected outcome for each investment ...4 marks 3. What investment would be preferred by the investor ....4 marks