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An article suggested that under some circumstances the distribution of waiting time X could be modeled with the following pdf. F(x; 8, T) = 6 Osx

An article suggested that under some circumstances the distribution of waiting time X could be modeled with the following pdf. F(x; 8, T) = 6 Osx

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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An article suggested that under some circumstances the distribution of waiting time X could be modeled with the following pdf. e - 1 1 - F(x; 8, T) = Osx<T otherwise (a) Graph f(x; 8, 80) for the three cases e = 3, 1, and 0.5 and comment on their shapes. f(x) f(x) 0 = 0.5 0.050 = 0.5 0.05 0.04 0.04 0.03 0.03 8 = 3 8 = 3 0.02 0.02 e = 1 0.01 0.01 20 40 60 80 20 40 60 80 f(x) f(x) 0 = 0.5 0 = 0.5 0.05 0.05 0.04 0.04 0.03 0.03 8 = 3 e = 3 0.02 0.02 e = 1 0.01 0.01 20 40 60 80 20 40 60 80 (b) Obtain the cumulative distribution function of X. xs 0 F(x) = 0 <x<T (c) Obtain an expression for the median of the waiting time distribution. (d) For the case 0 = 3, T = 80, calculate P(40 s Xs 70) without at this point doing any additional integration. (Round your answer to four decimal places.)
Transcribed Image Text:An article suggested that under some circumstances the distribution of waiting time X could be modeled with the following pdf. e - 1 1 - F(x; 8, T) = Osx<T otherwise (a) Graph f(x; 8, 80) for the three cases e = 3, 1, and 0.5 and comment on their shapes. f(x) f(x) 0 = 0.5 0.050 = 0.5 0.05 0.04 0.04 0.03 0.03 8 = 3 8 = 3 0.02 0.02 e = 1 0.01 0.01 20 40 60 80 20 40 60 80 f(x) f(x) 0 = 0.5 0 = 0.5 0.05 0.05 0.04 0.04 0.03 0.03 8 = 3 e = 3 0.02 0.02 e = 1 0.01 0.01 20 40 60 80 20 40 60 80 (b) Obtain the cumulative distribution function of X. xs 0 F(x) = 0 <x<T (c) Obtain an expression for the median of the waiting time distribution. (d) For the case 0 = 3, T = 80, calculate P(40 s Xs 70) without at this point doing any additional integration. (Round your answer to four decimal places.)
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