The time it takes to answer an exam question in a certain course is divided into the time (denoted as random variable X ) it takes to find the crucial idea, and the time (denoted as random variable Y ) it takes to perform all the calculations. Suppose X and Y are independent. (a) If X is exponentially distributed with parameter 0.5 and Y is uniformly distributed on the interval (7, 12), what is the probability that the total time to answer the question is less than 15 minutes? (b) If X is exponentially distributed with parameter 0.5 and Y is expo- nentially distributed with parameter 0.2, what is the probability density function of X + Y