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. Įkac² f(x) = 0≤x≤2 otherwise 0 (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) X 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 O O f(x) f(x) 1.5 1.5 LL 1.0 1.0 0.5 0.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 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 30 and 45 sec? (Round your answer to four decimal places.) (d) What is the probability that the lecture continues for at least 90 sec beyond the end of the hour? (Round your answer to four decimal places.) 1.5 1.0 0.5 X 1.5 1.0 0.5
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. Įkac² f(x) = 0≤x≤2 otherwise 0 (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) X 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 O O f(x) f(x) 1.5 1.5 LL 1.0 1.0 0.5 0.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 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 30 and 45 sec? (Round your answer to four decimal places.) (d) What is the probability that the lecture continues for at least 90 sec beyond the end of the hour? (Round your answer to four decimal places.) 1.5 1.0 0.5 X 1.5 1.0 0.5
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![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.
f(x) =
={10320
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)
X
1.0
1.5
2.0
1.0
1.5
1.5
1.5
1.0
1.0
0.5
0.5
X
X
0.5
1.0
1.5
2.0
0.5
1.0
1.5
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 30 and 45 sec? (Round your answer to four decimal places.)
(d) What is the probability that the lecture continues for at least 90 sec beyond the end of the hour? (Round your answer to four decimal places.)
1.5
1.0
0.5
O
f(x)
0.5
1.5
1.0
0.5
O
f(x)
0.5
2.0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8edd889e-338a-4275-872c-5b2b400b4e22%2F94ce311e-4429-4fae-9147-bba4312c1bc2%2Foiqe4g9_processed.png&w=3840&q=75)
Transcribed Image Text: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.
f(x) =
={10320
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)
X
1.0
1.5
2.0
1.0
1.5
1.5
1.5
1.0
1.0
0.5
0.5
X
X
0.5
1.0
1.5
2.0
0.5
1.0
1.5
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 30 and 45 sec? (Round your answer to four decimal places.)
(d) What is the probability that the lecture continues for at least 90 sec beyond the end of the hour? (Round your answer to four decimal places.)
1.5
1.0
0.5
O
f(x)
0.5
1.5
1.0
0.5
O
f(x)
0.5
2.0
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