There is a project with risk. There are two periods. In period $1,$ the entrepreneur does not observe the profitability $z$ and only know $z$ follows a binominal distribution:

$z=\{\begin{array}{ccc}-1,& \text{w}\text{i}\text{t}\text{h}\text{p}\text{r}\text{o}\text{b}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}& \frac{1}{2},\\ 3,& \text{w}\text{i}\text{t}\text{h}\text{p}\text{r}\text{o}\text{b}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}& \frac{1}{2}.\end{array}$

At the end of period $1,$ the entrepreneur knows its profitability z$.$ Assume this entrepreneur only has one chance to invest in the project. If the entrepreneur decides to invest, he has to pay a fixed cost of $0\mathrm{.}5.$ Assume there is no time discount and in each period the profit function is simply $y=z.$

Question: When should this entrepreneur invest, in period $1$ or wait until period $2?$

$2$