Q3. Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(- λx), and t and s are two positive numbers, use the definition of conditional probability to show that P(X > t + s | X > t) = P(X > s). Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)
Q3. Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(- λx), and t and s are two positive numbers, use the definition of conditional probability to show that P(X > t + s | X > t) = P(X > s). Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q3. Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(- λx), and t and s are two positive numbers, use the definition of conditional probability to show that
P(X > t + s | X > t) = P(X > s).
Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)
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