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. 0 ≤ x ≤ 2 f(x) = {kx² 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) 1.5 O 1.0 0.5 f(x) 1.5 1.0 0.5 X 0.5 1.0 1.5 2.0 X 0.5 1.0 1.5 2.0 1.5 1.0 0.5 f(x) 1.5 1.0 0.5 X 0.5 1.0 1.5 2.0 X 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 15 and 60 sec? (Round your answer to four decimal places.) (d) What is the probability that the lecture continues for at least 75 sec beyond the end of the hour? (Round your answer to four 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 as follows. 0 ≤ x ≤ 2 f(x) = {kx² 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) 1.5 O 1.0 0.5 f(x) 1.5 1.0 0.5 X 0.5 1.0 1.5 2.0 X 0.5 1.0 1.5 2.0 1.5 1.0 0.5 f(x) 1.5 1.0 0.5 X 0.5 1.0 1.5 2.0 X 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 15 and 60 sec? (Round your answer to four decimal places.) (d) What is the probability that the lecture continues for at least 75 sec beyond the end of the hour? (Round your answer to four decimal places.)
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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 as follows.
0 ≤ x ≤ 2
f(x)
= {kx²
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)
1.5
O
1.0
0.5
f(x)
1.5
1.0
0.5
X
0.5
1.0
1.5
2.0
X
0.5
1.0
1.5
2.0
1.5
1.0
0.5
f(x)
1.5
1.0
0.5
X
0.5
1.0
1.5
2.0
X
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 15 and 60 sec? (Round your answer to four decimal places.)
(d) What is the probability that the lecture continues for at least 75 sec beyond the end of the hour? (Round your answer to four decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbedd5747-9476-45b7-ab2c-0211874b0421%2Ff80bd466-3280-4bec-9ca9-9966a2d118fc%2Fqq8ge40k_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.
0 ≤ x ≤ 2
f(x)
= {kx²
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)
1.5
O
1.0
0.5
f(x)
1.5
1.0
0.5
X
0.5
1.0
1.5
2.0
X
0.5
1.0
1.5
2.0
1.5
1.0
0.5
f(x)
1.5
1.0
0.5
X
0.5
1.0
1.5
2.0
X
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 15 and 60 sec? (Round your answer to four decimal places.)
(d) What is the probability that the lecture continues for at least 75 sec beyond the end of the hour? (Round your answer to four decimal places.)
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