A (hypothetical) study is performed to estimate the effect of a simple training program on basketball free-throw shooting. A random sample of 100 college students is recruited into the study. Each student first shoots 100 free-throws to establish a baseline success probability. Each student then takes 50 practice shots each day for a month. At the end of that time, he or she takes 100 shots for a final measurement. Let be the average improvement in success probability. Give three prior distributions for (explaining each in a sentence)