The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35. (a) Determine the pdf of X. 1 25 V
The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35. (a) Determine the pdf of X. 1 25 V
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35.
(a) Determine the pdf of X.
1
25
<x s 35
f(x) =
10
otherwise
Sketch the corresponding density curve.
f(x)
f(x)
0.20-
0.20F
0.15
0.15
0.10
0.10
0.05
0.05
X
25
30
35
25
30
35
f(x)
f(x)
0.20|
0.20-
0.15
0.15
0.10
0.10
0.05
0.05
X
X
25
30
35
25
30
35
(b) What is the probability that preparation time exceeds 31 min?
(c) What is the probability that preparation time is within 3 min of the mean time? [Hint: Identify u from the graph of f(x).]
(d) For any a such that 25 < a < a + 3 < 35, what is the probability that preparation time is between a and a + 3 min?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86bfc21f-7304-4d6a-8ae3-de059a5180e7%2F31edb0db-594b-4cc8-b959-1ddbf1ca8f04%2Fuwz25uo_processed.png&w=3840&q=75)
Transcribed Image Text:The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35.
(a) Determine the pdf of X.
1
25
<x s 35
f(x) =
10
otherwise
Sketch the corresponding density curve.
f(x)
f(x)
0.20-
0.20F
0.15
0.15
0.10
0.10
0.05
0.05
X
25
30
35
25
30
35
f(x)
f(x)
0.20|
0.20-
0.15
0.15
0.10
0.10
0.05
0.05
X
X
25
30
35
25
30
35
(b) What is the probability that preparation time exceeds 31 min?
(c) What is the probability that preparation time is within 3 min of the mean time? [Hint: Identify u from the graph of f(x).]
(d) For any a such that 25 < a < a + 3 < 35, what is the probability that preparation time is between a and a + 3 min?
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