Continuous distribution exercises
1.
Clock A is more than two hours behind clock B. What’s the probability of this happening by chance? Assume these are grandfather clocks with 12 hour dials.
[Answer: 25/72]
2.
Joe and Mary randomly meet at the coffee house between 10:00 and 10:30. What’s the probability of Joe arriving more than 15 minutes after Mary?
[Answer: 1/8]
3.
Joe and Mary go a small store independently; Joe will be there between 10:00 and 10:30, while Mary will be there between 10:00 and 10:15. Assuming uniform distribution on the arrival time, what’s the probability they’ll be at the store at the same time?
[Answer: 1/2]
4.
Joe gets to the bus stop at a random time between 10:00 and 10:30 while Mary gets there at a random time between 10:20 and 10:40. What is the probability they meet at the bus stop if they go there independently? (Hint: use two 1-dimensional spaces plus the independence of the two events)
[Answer: 1/6]
5.
Stocks A and B oscillate randomly between 100 and 115 dollars. Assuming that their oscillations are independent of each other and that you paid 100 dollars for each one, what’s the probability you’ll make at least 20 dollars?
[Answer: 2/9]