I assume that the agent is an expected utility maximizer with Bernoulli index $$u$$, where $$b$$ and $$y$$ are fixed constants. Then, just take expectations of $$u$$ and try to write the right-hand side as function of the mean and variance of $$M$$.
For the risk aversion part, recall that an expected-utility maximizer is risk averse if his Bernoulli index $$u$$ is concave.