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 asfollows.kx Osxs 2f(x) =otherwise(a) Find the value of k. (Enter your answer to three decimal places.)0.375Draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.]f(x)f(x)1.51.51.01.00.50.50.51.01.52.00.51.01.52.0f(x)f(x)1.51.51.01.00.50.50.51.01.52.00.51.01.52.0(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.)0.125(c) What is the probability that the lecture continues beyond the hour for between 45 and 90 sec? (Round your answer to four decimal places.)

Introduction: Denote the random variable as X.

Answered: A college professor never finishes his…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.6: Quadratic Functions

Problem 38E

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Xavier and Yolanda both have classes that end at noon and they agree to meet every day after class. They arrive at the coffee shop independently. Xavier's arrival time is X and Yolanda's arrival time is Y, where X and Y are measured in minutes after noon. The individual density functions are given.(Xavier arrives sometime after noon and is more likely to arrive promptly than late. Yolanda always arrives by 12:10 PM and is more likely to arrive late than promptly.) After Yolanda arrives, she'll wait for up to 45 minutes for Xavier, but he won't wait for her. Find the probability that they meet. (Round your answer to three decimal places.)
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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