This is the whole question,. nothing else is provided. please show work.

Question 3. (10 points) Assume that the score you can get on the midterm or practice test is a random variable which can take only two values high (H) or low (L) Set the utility u(H) = 1 and u(L) = 0. The score that you get on the practice test depends on your choice of effort 0 S e g 1. To be more specic, with probability 6, you will get H, and with probability 1 6, you will get L on this homework. You (dis)utility of effort is e2, so, after you complete the practice test, your utility will be either 1 62 (with probability 6), or e2 (with probability 1 6). Next, assume that your performance on the midterm depends on the score that you achieve on the practice test, and no further effort is required. Namely, if you get H on the practice test, you get H on the midterm with probability (1H 6 (0, 1); and if you get L on the practice test, you get H on the midterm with probability (1;, 6 (0,1). Further, assume that (1;,