How do I solve part a-f. Please show work if you can.

1. Judge J must decide how to set bail for 4 criminal defendants, D1, D2, D3, and D4. The judge may choose bail for D; from the set B - {0, b;, B; }, where B, > b; > 0, and both 0 and b; would allow Di to be free pre-trial, while B; is too high to pay, thus D; would be detained pre-trial. Defendants strictly prefer lower bail amounts to higher bail amounts, and have some known probabil- ity (to J) that they are guilty, gi E [0, 1], and some unknown probability (to J) that they will commit a violent crime before their trial if they are released, v, c [0, 1]. Regardless of g, the judge would always prefer to release a defendant if they will not commit a violent crime pre-trial, but set bail at B; if they will commit a violent crime pre-trial. The judge's threshold for setting bail at B is if v; > o - 2. J knows that three of the defendants have v; - 0, and exactly 1 defendant has ; - 1, but they don't know which it is. (a) For any defendant Di, what is, IE(v;), the expected value of v;? (b) The v; you found in (a) should be below 7. Given this, briefly discuss whether you think the optimal policy is to release each defendant (set bail at 0 or b;), or to set bail at B; for each defendant, or something else. Now suppose J has access to a risk assessment algorithm (RSA) that tells if D; is "high risk", H, or 'low risk", L. The RSA works as follows . If the true vi = 0, then the RSA says L with probability 4/5, and H with probability 1/5. . If the true vi = 1, then the RSA says L with probability 1/10, and H with probability 9/10. (c) If J uses the RSA on defendant D, and it says L, how much more likely is it that D, has v; = 0 and not ; - 1? (HINT: this will be the odds ratio for L. If you want you can also use this to calculate the actual probability that v; - 0 if the RSA is L.) (d) If J uses the RSA on each defendant, briefly discuss whether you think the optimal policy is to release defendants (set bail at 0 or b;) if the RSA says L, and set bail at B; if the RSA says H, or something else. (e) Is the assumption that the judge cares only about ;, and not gi, a reasonable assumption? Briefly discuss whether you think g, should be part of the consideration. (f) If J chooses to release the defendant, is there ever a reason to set bail at b; instead of 0? Briefly discuss, and feel free to think about conditions that are not mentioned in the