Consider an investor who faces a decision whether or not to make an investment of $$1000.$ A value function of the following form represents the investor$$s preferences with respect to gains and losses

v$($x$)=$x for $$x $0$

$2$x for $$x $<0$

The investor$$s probability weighting function is

p$\backslash$gamma

w $($p$)=1/\backslash$gamma $,$

$($p$\backslash$gamma $+(1$ p$)\backslash$gamma $)$

Where the perception bias $\backslash$gamma equals $0\mathrm{.}5.$ The returns from the investment $($in $\%$ of the initial investment of $$1000)$ and their probabilities of occurrence p are given in the following table:

outcome p w$($p$)$

$-20\%30\%$

$0\%20\%$

$10\%30\%$

$40\%20\%$

$($a$)$ Calculate the values of the probability weighting function w$($p$).$

$($b$)$ Calculate the expected prospect theory return from investment.

$($c$)$ Determine whether the investor is likely to make the investment.