Suppose that a person plays a game in which he draws a ball from a box of 10 balls numbered 0 through 9. He then puts the ball back and continue to draw a ball (with replacement) until he draws another number which is equal or higher than the first draw. Let X denote the number drawn in the first draw and Y denote the number of subsequent draws needed.

(a) Find the conditional probability distribution of Y given X = x, for x = 0, 1, · · · , 9.
(b) Find the joint probability distribution of X and Y , P(X = x, Y = y).
(c) Find the probability distribution of Y , P(Y = y).
(d) Find E(Y ).

The probability distribution shows the probability of each possible outcome, zero through 15. That is, if you were to ask a total of 15 people to sample both Coke and Pepsi, the probability distribution you have created will show you the chance that any specific number of people will guess correctly. Print out the distribution and then respond manually to the following questions

1. What is the probability that 10 or more will identify correctly?

1. An airport limousine can accommodate up to 4 passengers on any one trip. The company will accept a maximum of 6 reservations for a trip, and a passenger must have a reservation. From previous records, 20% of all those making reservations do not show up for the trip. Answer the following questions assuming independence wherever appropriate.

   A) Assume that six reservations are made. Let X = the number of customers who have made a reservation and show up for the trip. Find the probability distribution function of X in table form.
2. B)Assume that six reservations are made. What is the probability that at least one individual with a reservation shows cannot be accommodated on the trip?
3. C)Assume that six reservations are made. What is the expected number of available places when the limousine departs?
4. Suppose that the probability distribution of the number of reservations made is given by the accompanying table. Let Y denote the number of passengers on a randomly selected trip.
5. D) Obtain the probability distribution function of Y in table form.The possible values for Y are 0, 1, 2, 3, 4. You are still assuming that 20% of passengers who have made a reservation do not show up.
6. E) Find the expected value of Y.

Suppose approximately 75% of all marketing personnel are extroverts, whereas about 65% of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the probability that all are extroverts? (b) In a group of 5 computer programmers, what is the probability that none are introverts? What is the probability that 3 or more are introverts? What is the probability that all are introverts?

Suppose approximately 80% of all marketing personnel are extroverts, whereas about 60% of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the probability that all are extroverts? (b) In a group of 4 computer programmers, what is the probability that none are introverts? What is the probability that 2 or more are introverts? What is the probability that all are introverts?

1. A factory manufactures machines. Each machine is defective with probability 1/100, independently.

The machines get numbered 1, 2, . . . as they’re produced
(a) Out of machines 1, . . . , 1000, what is the probability that none are defective?
(b) Out of machines 1, . . . , 1000, what is the probability that two or fewer are defective? (c) Out of machines 1, . . . , 1000, what is the probability that exactly ten are defective? (d) What is the probability that the first defective machine is number 17?
(e) What is the probability the first defective machine is numbered 18 or higher?

Suppose approximately 80% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the probability that all are extroverts? (b) In a group of 4 computer programmers, what is the probability that none are introverts? What is the probability that 2 or more are introverts? What is the probability that all are introverts?

Suppose the spot price of a bushel of wheat is $2.00, the annual storage cost is $0.30 per/bushel, the risk‐free rate is 8%, and the costs of transporting wheat from the destination point specified on the futures contract to a local grain elevator, or vice versa, is $0.01/bu.

a. Use the cost‐of‐carry model to determine the equilibrium price of a September wheat futures contract (expiration of T = 0.25).

b. Explain the arbitrage strategy an arbitrageur would pursue if the September wheat contract is trading at $2.16/bu.

1-5 Pitfalls to Avoid in Scientific Thinking 8. What types of misinterpretation result from confusing correlation and causation? Do any of the following statements involve fallacies? If so, which ones? Because sitting in the back of the classroom is correlated with getting lower grades in the class, students should always sit closer to the front of the classroom. Historically, the stock market rises in years the NFC team wins the Super Bowl and falls when the AFC wins the Super Bowl; I am rooting for the NFC team to win for the sake of my investment portfolio. Gasoline prices were higher last year than in 1970, yet people purchased more gas, which contradicts the law of demand...

1.       The social learning theory of Bandura emphasizes the importance of observing and modeling the behaviors, attitudes, and emotional reactions of others. Since most behavior is learned through observing others, we store this information for future guidance and actions. When answering the questions below, identify how and when social learning was part of the experience.   

1.       Identify skills you believe you possess.   

•             Communication

•             Ability to Work Under Pressure

•             Decision Making

•             Time Management

•             Self-motivation

•             Conflict Resolution

•             Leadership

•             Adaptability

•             Teamwork

•             Creativity

•             Responsible

•             Able to Operate Under Pressure

•             Efficient

•             Computer and Internet Skills

•             Verbal Communication

•             Organizational Skills

•             Multi-tasking

•             Time Management

1.       capabilities Choose a job posting in an area of interest and analyze it, with a focus on the workplace required of the candidate.

1.       The skills that match are the skills you can use to market yourself and set yourself apart from other job applicants.

2.       Determine which of the skills are most important to you. Write how you will verbally describe these skills during a future job interview.

3.       Create a Word document with your list of skills and a description of how you will verbally communicate them in an interview and an elevator speech. (An elevator speech is a brief summary.)