Answer the following questions using the information provided below and the decision tree. a$)$ What is the expected value of the optimal decision without sample information?

$

b$)$ If sample information is favourable

$($

F

$)$

$,$ what is the expected value of the optimal decision?

$

c$)$ If sample information is unfavourable

$($

U

$)$

$,$ what is the expected value of the optimal decision?