discrete probability distributions

Pernilles Super'Chip is a processor for super-fast image analysis. It is put into production in a factory. In this factory it turns out that the probability of a Super'Chip being defective is 2%. Consider the next 17 independent Super'Chips being produced.

tasks

a) Determine the expected number of defective Super'Chip. (Round your answer to 2 decimal places. )

b)  Determine the variance of the number of defective Super'Chip (Round your answer to 4 decimal places. )

c) Determine the standard deviation of the number of defective Super'Chip. (Round your answer to 2 decimal places. )

d) What is the probability that there is a maximum of 2 defective Super'Chip?  (Round your answer to 4 decimal places. )

e) What is the probability that there are exactly 8 Super'Chip if there are at least 2 defective Super'Chip? (Round your answer to 4 decimal places. )

A player of a video game is confronted with a series of opponents and has 77% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated. (a) What is the probability mass function of the number of opponents contested in a game? (b) What is the probability that a player defeats at least 3 opponents in a game? Round your answer to two decimal places (e.g. 0.98). (c) What is the expected number of opponents contested in a game? Round your answer to the nearest integer. (d) What is the probability that a player contests 4 or more opponents in a game? Round your answer to four decimal places (e.g. 0.9876). (e) What is the expected number of game plays until a player contests 4 or more opponents? Round your answer to the nearest integer.

For the following questions, find the probability using a standard 52-card deck. Write your answer as a fraction or with a colon in lowest terms.

1. Find the probability of drawing a face card.
2. Find the probability of drawing a black card.
3. Find the probability of drawing a red 10.
4. Find the probability of drawing a king.
5. Find the probability of not drawing a face card.
6. Find the probability of drawing a number less than 4.
7. Find the probability of drawing a 5.
8. Find the probability of drawing a black 2.
9. Find the probability of not drawing a red 8.
10. Find the probability of drawing an ace of spades.

Suppose that in a given round in an online market experiment, there are a 10 students assigned roles of sellers and 10 assigned roles as buyers. Altogether, they are assigned numbers 1,2,3....22. Each even numbered student is a buyer, and each odd numbered student is a seller. The costs of sellers are twice their student number. The value of buyers is his student number.

a) What is the market clearing quantity?

b) What is the highest possible market clearing price?

c) What is the lowest possible market clearing price?

1. Given the following fatty acids: Caproic Acid, Valeric Acid, Stearic Acid, Oleic Acid, Arachidonic Acid, Palmitic Acid, Cerebronic Acid, Timnodonic Acid and Cervonic Acid.

1a. Group them into saturated and unsaturated fatty acids. Identify the number of

carbons and number of double bonds, if present. Give their biochemical name.

1b. Arrange them based on their melting point, from lowest to highest.

1c. Which will you select as constituents of the cell membrane? Why?

Edith Educationer has a real problem with children’s television programs.  She believes there are too many commercials in them.  To study this, she collects a sample of 500 children’s programs (n = 500) and counts how many commercials are on during the program.  The frequency count of programs with the number of commercials is found below:  

Complete the table to produce the general discrete probability distribution (3.75 points).  Use this probability distribution to answer questions a – h.  

1. How many commercials, X, is the most likely outcome to occur?  
2. Find the average number and standard deviation of commercials a child will expect to see in a program.
3. What is the probability that a child will see 10 or more commercials when watching a program?  P(X ≥ 10)
4. What is the probability that a child will watch 4 commercials?  P(X <4)
5. What is the probability that a child will watch exactly 12 commercials?  P(X =12)
6. What is the probability that a child will watch exactly 7 commercials?  P(X =7)
7. What is the expected number of commercials in a program
8. Graph the probability Distribution

A bookstore at the Hartsfield-Jackson Airport in Atlanta sells reading materials (paperback books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.). A point-of-sale terminal collects a variety of information about customer purchases. Shown below is a table showing the number of snack items and the number of items of reading material purchased by the most recent customers. Reading Material 0 1 2 Snacks 0 0 66 15 1 237 81 36 2 123 33 9 a. Using the data in the table construct an empirical discrete bivariate probability distribution for number of snack items and number of reading materials in a randomly selected customer purchase. What is the probability of a customer purchase consisting of one item of reading materials and two items of snack? (to 3 decimals) What is the probability of a customer purchasing one reading material item only? (to 3 decimals) Why is the probability ? The probability because the point of sale terminal is only used when makes a purchase. b. Show the marginal probability distribution for the number of snack items purchased. Compute the expected value and variance (if required enter negative values as negative numbers). (to 2 decimals) (to 2 decimals) (to 2 decimals) (to 4 decimals) (to 4 decimals) Expected Value (to 2 decimals) Variance (to 4 decimals) c. What is the expected value and variance for the number of reading materials purchased by a customer? Expected Value (to 2 decimals) Variance (to 4 decimals) d. Show the probability distribution for total number of items in a customer purchase. Compute its expected value and variance (if required enter negative values as negative numbers). (to 2 decimals) (to 2 decimals) (to 2 decimals) (to 4 decimals) (to 4 decimals) 1 2 3 4 Expected Value (to 2 decimals) Variance (to 4 decimals) e. Compute the covariance and correlation coefficient between and (if required enter negative values as negative numbers). (to 4 decimals) (to 4 decimals) What is the relationship, if any, between the number of reading materials and number of snacks purchased on a customer visit?

Required:

• Ensure you show all formulas and state values of variables, substitute and solve.

• Provide a concluding statement for all parts.

1. Suppose that 31% of families in town own iPads. If sixteen families are surveyed at random,

   1. Determine the probability that exactly 4 families own an IPAD.

2. 2. Determine the probability that less than 3 families own iPads.

3. 3. Determine the probability that least 3 families own iPads.

4. 4. Determine the expected number of families with an iPad.

2. There are ten cats and eleven dogs in a pet shop. Nine pets are chosen at random to visit a children’s hospital.

1. 1. Determine the probability that exactly three of the pets will be dogs.

2. 2. Determine the probability that less than 2 of the pets will be dogs.

3. 3. Determine the probability that at least 2 of the pets will be dogs.

4. 4. Determine the expected number of dogs chosen.

Mike is a major league pitcher. He pitches like a robot, that is he pitches the same way to each batter. There is a .56 probability that the first ball he pitches to a batter is a strike. (first-pitch strike). This is independent from batter to batter. Let X equal the number of first-pitch strikes Mike throws in a game where he pitches to 15 batters. Let Y equal the number of batters he pitches to until he throws his 2nd first-pitch strike. (could be more than 15)

a. What is the probability X=13?
b. What is the standard deviation of X?
c. What is the probability that X > 10?
d. What is the probability that X ≥ 12?
e. What is the probability that Y = 3?
f. What is the probability that Y = 2?

C Programming

The score table will be printed by reading the match information made between the teams.

It is not known how many teams. The team information will be kept in a dynamically changed memory area as the new team enters. The match list should also be kept in a dynamic area that is recorded as new match information is entered.

There should be 2 structs in the program.

Mac struct: Consists of 1st team name, 2nd team name, 1st team goal, 2nd team goal information.

Team struct: consists of team name (one word, 20), number of wins, number of draws, number of defeats, number of goals scored, number of goals eaten, point.

Example input: abc xyz 3 1 (Information will be entered completely and correctly.)

A single line of match information, with a space between them, 1 Team name, 2 Team name, 1.

The goal scored by the team will be entered as the goal scored by the 2nd team. In the case where the above example is the first match information entered for these teams, two teams will be identified in the abc and xyz names, and will be added to the team list, since there are no teams defined in these names yet. At the same time, a match struct will be defined, this match struct will be added to the match list, and all information of both teams in the team struct will be updated with this match information.

If the above example is not the first match information entered about the abc and xyz teams, since both teams will be defined before, these teams will be found in the teams list and their relevant information will be updated.

In summary, for the above entry, if the team has not yet been identified in these names, both teams will be identified and added to the team list. The number of victories of the ABC team will be increased by one, the number of goals scored will be increased by 3, the number of goals scored will be increased by 1, and the score will be increased by 3. The xyz team's number of defeats will be increased by 1, the goal scored will be increased by 1, the goal it has scored will be increased by 3, its score will be reduced by 1. (wins 3 points, draw 1 point, defeat -1 point). The match struct will be added to the match list.

After entering the match information, the scoreboard will be printed.

Scoreboard: The information in the team struct will be printed one after the other in the order given in the description. The scoreboard should be in descending order according to the score. In case of score equality, the team with a high average score (goals scored and goals scored) should be on the top. It can be assumed that the score and average will not be equal teams.

After the scoreboard is printed, the user will receive a sequence number from 1-teamnumber, and the matches of the team in the row entered will be listed. Unless -1 is entered, the sequence number will be read again after printing the information of a tool, and the program will end when -1 is entered. If a number between 1-teamnumber or an entry other than -1 has been made, an appropriate message will be given and the entry will be waited again.