2. Caroline and Sarah have agreed to meet between 5:30pm and 6:30pm for dinner at Witherspoon street. Let X be Caroline's arrival time (in the unit of minutes) and Y be Sarah's arrival time (in the unit of minutes), relative to 6:00pm. Assume that their arrival times are independent. What is the joint pdf of X and Y, if X and Y are normally distributed as N(0, 10²). If they can wait each other for 10 minutes, what is the probability that they actually meet? What is corr(X+Y,Y)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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2. Caroline and Sarah have agreed to meet between 5:30pm and 6:30pm for dinner at Witherspoon street.
Let X be Caroline's arrival time (in the unit of minutes) and Y be Sarah's arrival time (in the unit of
minutes), relative to 6:00pm. Assume that their arrival times are independent.
What is the joint pdf of X and Y, if X and Y are normally distributed as N(0, 10²). If they can
wait each other for 10 minutes, what is the probability that they actually meet?
What is corr(X + Y,Y)?
Transcribed Image Text:2. Caroline and Sarah have agreed to meet between 5:30pm and 6:30pm for dinner at Witherspoon street. Let X be Caroline's arrival time (in the unit of minutes) and Y be Sarah's arrival time (in the unit of minutes), relative to 6:00pm. Assume that their arrival times are independent. What is the joint pdf of X and Y, if X and Y are normally distributed as N(0, 10²). If they can wait each other for 10 minutes, what is the probability that they actually meet? What is corr(X + Y,Y)?
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