need asap 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 thehour and the end of the lecture and suppose the pdf of X is as follows.0≤x≤2f(x) =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 1.1f(x)f(x)1.51.00.5O0.51.01.52.0X1.51.00.5O0.51.01.52.0 XO190.5Of(x)DETAILS1.51.00.50.50.51.01.01.51.52.0DEVORESTAT9 4.1.0012.0X0.5Of(x)1.5-1.00.50.50.51.01.01.51.52.02.0(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.)X(c) What is the probability that the lecture continues beyond the hour for between 30 and 75 sec? (Round your answer to four decimal places.)(d) What is the probability that the lecture continues for at least 105 sec beyond the end of the hour? (Round your answer to four decimal places.)ASK Y

As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Answered: (b) What is the probability that the…

A First Course in Probability (10th Edition)

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Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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 f(x)= {kx2O < x < 2} 0 otherwise a. Find the value of k and draw the corresponding density curve.[ Hint: Total area under the graph of f (x) is 1.] b. What is the probability that the lecture ends within 1min of the end of the hour? c. What is the probability that the lecture continues beyond the hour for between 60 and 90 sec? d. What is the probability that the lecture continues for at least 90 sec beyond the end of the hour?

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(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 30 and 75 sec? (Round your answer to four decimal places.)