Suppose a college professor never finishes her lecture before the end of the classperiod, and always finishes within three minutes after the class period is supposed to end.Let X = time that elapses between the end of the class period and the actual end of the6.lecture. Suppose the pdf of X isf (x) = kx? 0 < x< 3 and 0 otherwise.Find the value of k that makes f(x) a legitimate probability density function, and use thatvalue of k to find the probability that the lecture ends within 1 minute after the class period issupposed to end.

We know that the total probability is always 1.Using that we…

6. Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within three minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is f(x) = kx² 0 < x < 3 and 0 otherwise. Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends within 1 minute after the class period is supposed to end.

6. Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within three minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is f(x) = kx² 0 < x < 3 and 0 otherwise. Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends within 1 minute after the class period is supposed to end.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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