A college professor always finishes his lectures within 2 minutes after the bell rings to end the period and the end of the lecture. Let X= the time that elapses between the bell and the end of the lecture and suppose the pdf of X is kx², if 0

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 27SE: Prove that bx=exln(b) for positive b1 .
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A college professor always finishes his lectures within 2 minutes after the bell rings to end the period and the end of the lecture. Let X=
the time that elapses between the bell and the end of the lecture and suppose the pdf of X is
f(x) = 10,
Skx², if 0 < x< 2,
otherwise.
a. Find the value of k. [Hint: Total area under the graph of f(xr) is 1.
b. What is the probability that the lecture continues beyond the bell for between 60 and 90 seconds?
Transcribed Image Text:A college professor always finishes his lectures within 2 minutes after the bell rings to end the period and the end of the lecture. Let X= the time that elapses between the bell and the end of the lecture and suppose the pdf of X is f(x) = 10, Skx², if 0 < x< 2, otherwise. a. Find the value of k. [Hint: Total area under the graph of f(xr) is 1. b. What is the probability that the lecture continues beyond the bell for between 60 and 90 seconds?
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