1. PROBABILITY AND STATISTICS
WEEK 7
Onur Doğan

2. Quiz Q1
How many positive integer solutions are there to the equation x+y+z=12?
Onur Doğan

3. Quiz Q2
After all students have left the classroom, a statistics professor notices that three bags were left under desks. At the beginning of the next lecture, the professor distributes the three bags in a completely random fashion to each of the three students who claim to have left bags. Let X denote the number of students who receive their own bag. Determine the pmf of X.
Onur Doğan

4. Quiz Q3
The pmf for X=the number of major defects on a randomly selected appliance of a certain type is
Calculate the E(X) and V(X).
Onur Doğan

5. Quiz Q4
Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products, 60% of moderately successful products, and 10% of poor products received good reviews. In addition, 40% of product designs have been highly successful, 35% have been moderately successful, and 25% have been poor products.
i.Find the probability that a product receives a good review.
ii.What is the probability that a new design will be highly successful if it receives a good review?
Onur Doğan

6. Binomial vs Hypergeometric
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7. Onur Doğan

8. Binomial vs Hypergeometric
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9. Example
A basketball player has a free throw percentage of 70%. In a single game, the player shoots 6 free throws. Compute the following probabilities.
i. What is the probability that she makes exactly 3?
ii. What is the probability that she makes at least 5 successful throws?
İii.What is the probability that she makes all 6?
Onur Doğan

10. Example
During a particular period a university’s information technology office received 20 service orders for problems with printers, of which 8 were laser printers and 12 were inkjet models. A sample of 5 of these service orders is to be selected for inclusion in a customer satisfaction survey. What’s the probability of 2 of the selected printers are inkjet models?
Onur Doğan

11. Example Products produced by a machine has a 3% defective rate.
i.What is the probability that the first defective occurs in the fifth item inspected?
ii.What is the probability that the first defective occurs in the first five inspections?
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12. Example
A team is currently winning 0,6 of their games. There are 5 games in November. What is the probability that the team will win more games than they lose?
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13. Example
A person conducting telephone surveys must get 3 completed surveys before their job finished. There is 0,1 chance of reaching a person who will complete the survey. What is the probability the 3 completed survey occurs on the 10th call?
Onur Doğan