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You have two friends: a reliable friend, and an unreliable friend. When the reliable friend says "I'll be there in 5 minutes", what this means is "I'll be there in X minutes, where X~ Uniform(0,5)". When the unreliable friend says "I'll be there in 5 minutes", what this means is "I'll be there in Y minutes, where Y~ Exponential()". (X and Y are independent.) You ask your friends for help and they both say "I'll be there in 5 minutes." What is the probability that the reliable friend arrives first? Set up an integral; do not evaluate.

You have two friends: a reliable friend, and an unreliable friend. When the reliable friend says "I'll be there in 5 minutes", what this means is "I'll be there in X minutes, where X~ Uniform(0,5)". When the unreliable friend says "I'll be there in 5 minutes", what this means is "I'll be there in Y minutes, where Y~ Exponential()". (X and Y are independent.) You ask your friends for help and they both say "I'll be there in 5 minutes." What is the probability that the reliable friend arrives first? Set up an integral; do not evaluate.

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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You have two friends: a reliable friend, and an unreliable friend. When the reliable friend says "I'll be there in 5 minutes", what this means is “I'll be there in X minutes, where X ~ Uniform(0,5)". When the unreliable friend says "I'll be there in 5 minutes", what this means is "I'll be there in Y minutes, where Y~ Exponential()". (X and Y are independent.) You ask your friends for help and they both say "I'll be there in 5 minutes." What is the probability that the reliable friend arrives first? Set up an integral; do not evaluate.
Transcribed Image Text:You have two friends: a reliable friend, and an unreliable friend. When the reliable friend says "I'll be there in 5 minutes", what this means is “I'll be there in X minutes, where X ~ Uniform(0,5)". When the unreliable friend says "I'll be there in 5 minutes", what this means is "I'll be there in Y minutes, where Y~ Exponential()". (X and Y are independent.) You ask your friends for help and they both say "I'll be there in 5 minutes." What is the probability that the reliable friend arrives first? Set up an integral; do not evaluate.
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