ECON 3400
FINAL EXAM
24 MAY 2022
Arash Pourebrahimi
Submit your answers as one PDF or Word file on blackboard.
** Do not upload Pages files **
*** Write your full name at the top of your answer sheet***
Due time: Submit your answers no later than 5:45 pm.
QUESTION 1) Consider the following European Roulette:
The wheel picks a number from 0 to 36 randomly. For each possible outcome, your payoff is as follows:
| Outcome | Payoff |
| A number between 1 and 24 (Including 1 and 24) | You win $400 |
| A number between 25 and 36(Including 25 and 36) | You win or lose nothing. Pay off is 0. |
| 0 | You lose $1000 |
1A) Calculate the expected value of this game
1B) Calculate the variance and the standard deviation of this game*
* Show your work, and calculate final numbers.
2) How can you double the expected value of the game in question 1 without changing the variance? Elaborate your answer.
3) Consider the same European Roulette we saw in question 1, give an example of two disjoint events based on this game.
4) Still consider the same Roulette. Suppose you play it once. Calculate the following probabilities:
4A) The wheel picks a red AND even number.
4B) The wheel picks a red OR even number.
(Show your answers as fractions only)
5) Still consider the same Roulette. Suppose you play it three times. What is the probability of having AT LEAST one red outcome?
(Show your answers as fractions only)
6) You have a shop. Each customer who enters your shop makes the following decisions with given probabilities independent from other customers:
| Outcome | Probability |
| No purchase | 40% |
| Purchasing one item | 25% |
| Purchasing two items | 30% |
| Purchasing more than two items | 5% |
6A) What is the probability that your first sale of the day is by the 5th customer that enters your shop.
6B) To have your first sale, how many customers one average should enter your shop?
6C) If 100 customers enter your shop, how many of them would purchase one or more items from you? (Tell your expectation)
6D) If 150 customers enter your shop, what is the probability that 60 of them purchase one or more items from you.
*(Fractions are enough, no need to calculate the final answer)
*(If you use combination formula, you need to show it with factorials at least).
7) USA soccer team plays against United Kingdom in the World Cup. Because of that, US officials want to play four friendly matches against four different countries from the European Union. All matched are held in the US, and the order of matches is not important. Note that the European Union has 28 members, and the UK is not in the EU.
7A) How many different combinations of four matches can possibly be organized?
7B) US officials do not want to play against Hungary, but they want to make sure that there is a match against Germany. How many different combinations of four matches can possibly be organized now?
*(Fractions are enough, no need to calculate the final answer)
*(If you use combination formula, you need to show it with factorials at least).