A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour Let X the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows kx 0 x 2 otherwise a Find the value of k Enter your answer to three decimal places Draw the corresponding density curve Hint Total area under the graph of f x is 1 f x f x 1 5 1 0 0 5 f x 1 5 1 0 0 5 0 5 0 5 1 0 1 0 1 5 1 5 2 0 2 0 X 1 5 3197633301 1 0 0 5 f x 1 5 1 0 0 5 0 5 0 5 1 0 1 0 1 5 1 5 2 0 2 0 b What is the probability that the lecture ends within 1 min of the end of the hour Enter your answer to three decimal places c What is the probability that the lecture continues beyond the hour for between 60 and 90 sec Round your answer to four decimal places X X Page 2 of 11