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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 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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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?
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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