10x) = {1x²2 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)
10x) = {1x²2 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)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 70E
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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.
Skx² 0≤x≤2
otherwise
(a) Find the value of k. (Enter your answer to three decimal places.)
P(x) = {10²2
Draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.]
f(x)
f(x)
1.5
1.0
0.5
O
f(x)
1.5
1.0
F
0.5
0.5
0.5
1.0
1.0
1.5
1.5
WebAssign Plot
2.0
2.0
1.5
1.0
0.5
O
f(x)
1.5
1.0
0.5
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
X
(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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4147167-787a-4124-9c1a-9473ac425578%2Fbf859eff-aecd-4f22-a8b5-f51fd9e0d8d4%2Fpghttwl_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.
Skx² 0≤x≤2
otherwise
(a) Find the value of k. (Enter your answer to three decimal places.)
P(x) = {10²2
Draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.]
f(x)
f(x)
1.5
1.0
0.5
O
f(x)
1.5
1.0
F
0.5
0.5
0.5
1.0
1.0
1.5
1.5
WebAssign Plot
2.0
2.0
1.5
1.0
0.5
O
f(x)
1.5
1.0
0.5
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
X
(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.)
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