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Practice Problem: What is the probability that a meeting will occur?
A student and a professor agree to meet in the MSEE atrium at 2pm to go over the homework. Let X be the arrival time of the student, and let Y be the arrival time of the professor. Assume that the 2D random variable (X,Y) is uniformly distributed in the square [2 , 3]x[2,3].
If the student arrives first, then he will wait up to 20 minutes for the professor to arrive: if the professors does not show up within that time frame, then the student will leave.
The Professor is more impatient: she will leave if she has to wait for more than 10 minutes for the student to arrive.
What is the probability that the meeting will occur?
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
Hint:
- Assume the time the student shows up is X.
- Assume the time the professor shows up is Y.
- Two equations that must be satisfied to have the meeting occurs: we represents the time unit in hour
- 1. $ Y \leq X + \frac{1}{3} $
- 2. $ X \leq Y + \frac{1}{6} $
- Find the area bounded by the equations and the range of X and Y. (You can shift the range of X and Y from [2,3]x[2,3] to [0,1]x[0,1] for easier calculation) -TA
Answer 2
Write it here.
Answer 3
Write it here.
