Problem 2: The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by f(x) = ( C x2 x > 12 0 x ≤ 12 (a) Find the constant C and P(X > 20). (b) What is the cumulative distribution function of X? (c) What is the probability that of 6 such types of devices at least 3 will function for at least 15 hours? What assumptions are you making? (d) Let Y be the lifetime of the same device measured in minutes. What is the probability density function of Y ?