Problem $2$: Rank Dependent Utility $(Referto$ Slides $13-19in$ Module $12)(6$ points$)$

Consider the following decision between two alternatives $a^{\text{'}}$ and $a^{\text{'}\text{'}}.$

The decision maker's utilities for the outcomes are $as$ follows:

$u(x_1)=1\mathrm{.}0,u(x_2)=0\mathrm{.}7,u(x_3)=0\mathrm{.}5,u(x_4)=0\mathrm{.}25,u(x_5)=0\mathrm{.}15,u(x_6)=0\mathrm{.}05$

Assume that the decision maker follows Rank Dependent Utility $(RDU)$ with $w(R)=R^2.$ Calculate the

Rank Dependent Utility $(RDU)$ for the two alternatives. Which alternative will the decision maker choose?

$Is$ the decision consistent with what you obtained using the expected utility theory?