4. A physical education student is studying the effect of a simple training program on basketball free-throw shooting. She recruits a random sample of 100 college students to participate in her study. Each student rst shoots 100 freethrows to establish a baseline success probability. Each student then takes 50 practice shots each day for a month. At the end of that time, each student takes 100 shots for a nal assessment. Let K: denote the ith student's difference between their accuracy rate (shots made/ 100) after the program and their accuracy rate before the program, where \"the program\" is taking 50 practice shots each day for a month. Assume that \"id . . each Y} N NW, 0'2) where 6' 18 an unknown parameter and 0'2 18 a known number. a. Give a prior distribution for 6' using a diffuse (vague) prior. Explain your choice in a sentence or two. b. Give a subjective prior distribution for 9 using your knowledge of the problem. Again, explain your choice in a sentence or two