Assume the hour hand of broken clock is stuck pointing at 12 and that the minute hand can be spun at will. Suggest spinning the minute hand and then measuring the angle? It makes with the hour hand when it comes to the stop. Let ? be measured so that it always lies between 0 and 180 degrees. Suppose that the minute hand spins "fairly," in that after spinning, it is no more likely to point in any particular direction than another.
(a) Compute the probability density function for random variable? Be sure to specific where this function takes the value 0.
(b) Employ your answer to part (a) to find out the probability that the minute hand will end up between 45 and 90 degrees from hour hand.