You are proposed to accept or reject a lottery which gives X with probability 1/3 and -1 with probability 2/3. Before accepting you receive a signal "g" (good) or "b" (bad). The signal has precision q=P(g|win)=P(b|lose)>1/2.
Suppose you choose between accepting and rejecting the lottery without the signal. What is the value of your choice V (X) as a function of
X? In other words, this is the value you get taking your choice into account. Draw V (X) on a graph.
Now suppose you take signal into account. What is the value Vs(X) of your choice before you see the signal? Draw it on the graph.
What is the value of the signal as a function of X. Specify and draw it on the graph.