If invest $1000 initially, consider a world of only two future states with equal probability. The payoffs are:

|Investment | state 1| state 2|

|Investment 1 |800| 1200 |

|Investment 2 | 800| 1000 |

|Investment 3 |600| 1200 |

If utility function has conventional property of U'(x)>0 and U''(x)<0, which of the following statements are true?

Select one or more:

a.investment 2 state-by-state dominates investment 1 and 3

b.investment 2 second order stochastically dominates investment 1

c.investment 1 second order stochastically dominates investment 2

d.investment 1 first order stochastically dominates investment 2

e.investment 2 second order stochastically dominates investment 3

f.investment 3 first order stochastically dominatesinvestment 2.