An investor whose initial wealth is $1,000 is offered an opportunity to play a fair game with two possible outcomes: winning $200 with probability of 1/2 or losing $200 with probability of 1/2. This investors utility function equals the natural logarithm of wealth, U (W) = ln (W). Determine E[U(W_T)] and U (E[W_T]), where W_T is the terminal wealth. What is the investors attitude toward risk?

# Please give the solutions with steps, don't just tell me the concept and steps and ask me to solve it.