Chapter 8: separate solutions

Question 1

Compute default posterior.

[0.5*0.9,0.5*0.1]/0.5=[0.9,0.1].

Question 2

What observation cost makes default information break even?

Acting now has expected reward 0.5(10)+0.5(-10)=0. After either observation the posterior is [0.9,0.1] or its mirror image, so the best action has expected reward 0.9(10)+0.1(-10)=8. The gross value of information is 8, so information breaks even at an observation cost of 8 utility units.

Question 3

Compute transfer posterior after observation 1.

[0.12,0.28]/0.4=[0.3,0.7].