(9 Marks) The length of time required by students to complete a onehour exam is a random variable with a probability density function (pdf) given by f (as) = 0x3 + 332, 0 S X 1. a) Find the value c and write down the new pdf. (2 points) b) Find the probability that a randomly selected student will finish in less than half an hour. (3 points)c) Find the mean and standard deviation of the distribution. (4 points)