What is the probability of receiving 6 emails from your students in next hour?
10 May 2022
Submit your answers as one PDF file on blackboard no later than 6:00 pm.
1- Suppose that you roll a fair dice (so the outcome can be an integer from 1 to 6, and each possible outcome has the same likelihood). In this game, you can win or lose money in this game depending on the outcome. Here is the payoffs table (negative numbers mean you lose money).
1a) Calculate the expected value of this game*
2a) Calculate the variance and the standard deviation of this game*
3a) Do you think it is a good idea to play this game? Why?
* For parts 1a and 2a, show your work, and calculate final numbers.
2- Suppose that we add $300 to the payoffs of question 1, now calculate the new expected value, standard deviation, and variance of the game (show your work, no need to calculate final numbers).
3- Suppose that we double the payoffs of question 1, now calculate the new expected value, standard deviation, and variance of the game (show your work, no need to calculate final numbers).
4- Define a Bernoulli trial (whatever you like). So, you need to define a trial and then explain what success and failure are. Then assign numbers to the probability of success and the probability of failure (you can use your imagination when you assign probabilities).
5- For your mid-term project, I decided to audit 4 students to make sure that they did their project individually. That means I will meet those students online and will ask them to explain their projects to me (do not worry, it’s an imaginary situation). I choose 4 students randomly. There are 35 students in this class.
5a) Calculate in how many ways I can choose four students out of 35 students.
5b) Suppose that I am so suspicious about your midterm project, so I decided to select you for the audition for sure. Now calculate in how many ways I can choose those 4 students (one of them is you).
(Show your work. Fractions with factorials are enough, no need to calculate the final answer)
6- Valeriia starts using a dating app called Tinder. The app works this way: you see a profile; if you swipe right on someone and that person swipes right on your profile too, you match. For each person on whom Mina swipes right, the probability that they match is 30%, and the probability of matching with each person is independent of the probability of matching with another person.
6a) What is the probability that Valeriia’s first match is with the 8th person on whom she swiped right? (Geometric model)
6b) On how many people should Valeriia swipe right on average to get her first match? (Geometric model)
6c) what is the expected number of Valeriia’s matches if she swipes right on 100 persons? (Binomial model)
6d) What is the probability of having 50 matches if she swipes right on 100 persons? (Binomial model)
(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) Suppose that you are a teacher and you receive 8 emails from your students per hour.
7a) What is the probability of receiving 6 emails from your students in next hour?
7b) What is the probability of receiving more than 2 emails in the next hour? (you need to be creative for this one)
– Use Poisson model
(Just right the formula, no need to calculate anything)