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Q12. The median of a random variable X is any value a for which P(X ≤ a) ≥ 1/2 and P(X ≥ a) ≥ 1/2. Now suppose that the arrival time X (in seconds) of tasks arriving into a server follows exponential distribution with parameter λ = 3. (a) Determine the median of X. Round your answer to 4 decimal places, if necessary. (b) Compare the median to the expectation of X. Which value is higher, given that e≈ 2.7183?

Q12. The median of a random variable X is any value a for which P(X ≤ a) ≥ 1/2 and P(X ≥ a) ≥ 1/2. Now suppose that the arrival time X (in seconds) of tasks arriving into a server follows exponential distribution with parameter λ = 3. (a) Determine the median of X. Round your answer to 4 decimal places, if necessary. (b) Compare the median to the expectation of X. Which value is higher, given that e≈ 2.7183?

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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Q12. The median of a random variable X is any value a for which P(X ≤ a) ≥ 1/2 and P(X ≥ a) ≥ 1/2. Now suppose that the arrival time X (in seconds) of tasks arriving into a server follows exponential distribution with parameter λ = 3. (a) Determine the median of X. Round your answer to 4 decimal places, if necessary. (b) Compare the median to the expectation of X. Which value is higher, given that e≈ 2.7183?
Transcribed Image Text:Q12. The median of a random variable X is any value a for which P(X ≤ a) ≥ 1/2 and P(X ≥ a) ≥ 1/2. Now suppose that the arrival time X (in seconds) of tasks arriving into a server follows exponential distribution with parameter λ = 3. (a) Determine the median of X. Round your answer to 4 decimal places, if necessary. (b) Compare the median to the expectation of X. Which value is higher, given that e≈ 2.7183?
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