Answer the following questions using the information provided below and the decision tree. P(81) = 0.68 P(F | 81) = 0.66 P( U82) = 0.56 d. S:F $3,800 SIF -$500 S, IF With Sample Information $4,500 SIE -$1,200 $. U $3,800 d. S2U -$500 U SU $4,500 S2V -$1,200 $3,800 Sa Without Sample Information -$500 Si $4,500 S2 -$1,200 a) What is the expected value of the optimal decision without sample information? a) What is the expected value of the optimal decision without sample information? $ Calculate the required posterior probabilities accurate to 3 decimal places. Do not round intermediate calculations. b) If sample information is favourable (F), what is the expected value of the optimal decision? $ c) If sample information is unfavourable (U), what the expected value of the optimal decision? $ d) What is the expected value with sample information, EV with SI? $ e) Calculate EVSR f) Based on your EVSI, should you pay $110 for the sample information? no yes