BSM Probability Spring, 2010

## Probability, Spring 2010

Budapest Semesters in Mathematics

 Márton Balázs Email: balazs@math.bme.hu Tel: 463 1111, ext. 5904 Office outside BSM: Budapest University of Technology and Economics (BME) (just in case) Office 3a, fifth floor, Building H, 1 Egry József u., 1111 Budapest Text is: A First Course in Probability, Seventh Edition by S. Ross Classes: M 12:15 - 1:00pm, F 12:15 - 1:45pm, Room 206 Make-up class: March 22 Monday, 8:30 - 10:00am, room B104 Office hour: M 1:15pm - 2:00pm, Room 206 Final exam: May 21 Friday, 12:15pm, Room 206

 The updated syllabus containing the course requirements. (Here is the old one, from before March 9.)   Here is last year's final, just for you to see how a final looks like.   Here is an ad to demonstrate that probability is useful and interesting. (Not to mention the steadily increasing number of open positions in probability and applications in the industry.) Among others, we'll cover the following questions:   What are the chances that there is no common birthday in a classroom?   The king comes from a family of two children. What is the probability that the other child is his sister? (Of course, not 1/2.)   The famous Monty Hall paradox (also featured in the series "Numbers"): Out of three doors, one hides treasure, two hide goats. You point to one of the doors, now Monty opens another door with a goat. Do you now think the treasure is behind your door, or behind the other one Monty did not open for you?   How certain should an inspector be when a new evidence occurs?   How worried should I be after a positive HIV test?   Maybe Murphy was right? (Anything that can go wrong, will go wrong.)   Does a fox have any chance of escaping a hunter?   Where would you place the service stations for a bus route that travels between cities A and B?   Does a bus driver usually see more or less passengers than a passenger on the bus? Why?   What does it mean to be completely memoryless?   Would you rather fly a three-engine plane or a five-engine one?   How many chocolate chips should you plan per muffin so that less than 1% of customers get upset?   What are the chances that you can shoot a bullet out of the forest without hitting a tree?   How can we measure the value of π just by flipping a needle?   For how long will Jack and Jill wait for each other on a rendez-vous?   Eight students enter the elevator in a ten-storey building. How many times will the elevator stop?   How much time does it take for the lost miner to find his way out of the mine?   Upon receiving a noisy signal, what is your best guess for what has been sent?   How will Sindbad try to select the nicest of the odalisques?   How many people should we ask when we make a survey?   The standard normal distribution in pdf.   Here you can find how the previous semester was taught.