Two buyers bid in an auction for a single object. Each can bid any integer amount from $0 to $10. The two bids are made simultaneously and independently of each other. The buyers’ respective values are v1 = 5 and v2 = 10. The bidder with the higher bid wins (obtains the object) and pays the amount of his own bid. However, the bidder who does not win the auction and thus does not get the object is also obliged to pay half of his own bid. In case of a tie in the bids bidder 2 wins.

(a) Specify the best responses to pure strategies for both bidders.

(b) Identify the pure strategy NE of the game.

(c) Find all dominated strategies for each bidder.

(d) Now restrict the possible bids to $4 and $5, and identify all pure and mixed strategy NE in this game.

Particle in a box: given the number of carbon atoms, and the wavelength. How do I find the highest filled orbital, the lowest unoccupied orbital, and the box length. (ex. # of C atoms = 4, wavelength = 508.9nm. HFO = ?, LUO= ?, Box length = ?nm

L=√[(hʎ/8mc) (n^2-n^2 )] I believe I need to use this equation to find the box length. I just don't know how to find what the n values are.

Suppose that the probability that a passenger will miss a flight is 0.0978. Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be​ "bumped" from the flight. Suppose that an airplane has a seating capacity of 51 passengers.

​(a) If 53 tickets are​ sold, what is the probability that 52 or 53 passengers show up for the flight resulting in an overbooked​ flight?

​(b) Suppose that 57 tickets are sold. What is the probability that a passenger will have to be​ "bumped"?

​(c) For a plane with seating capacity of 51 ​passengers, how many tickets may be sold to keep the probability of a passenger being​ "bumped" below 55%?

1.) The probability of an overbooked flight is

2.) The probability that a passenger will have to be bumped is

3.)The largest number of tickets that can be sold while keeping the probability of a passenger being​ "bumped" below

5​% is

Person1, Person2, and Person3 all play on the Lacrosse Team and have an upcoming game. If none of them play in the game, their team will win by 5 points. If exactly one of person1, person2, or person3 plays, their team will win by 6 points, if exactly two of them play, their team will win by 7 points, and if all three play, their team will win by 8 points.

The probability that person1 plays is 3/10, as is the probability that person2 plays and the probability that person3 plays. The probability that person1 plays if person3 plays is 1/2. The probability that person2 plays if person3 plays is 1/3. The probability that person2 plays if person1 plays is 4/10. The probability all three play is 1/20.

Find the expected value, variance, and standard deviation of the number of points they will win by.

. A person has two meetings schedule in a day. The probability she is late for the first

meeting is 0.4, the probability she is late for the second is 0.5, and the probability

she is late for both meetings is 0.3.

Please explain with where each number comes from and the meaning of formulas used if possible, thank you!

a) Is the event that she is late for the first meeting independent of the event that

she is late for the second meeting? Explain

b) Are the two events disjoint? Explain

c) What is the probability that she is late for at least one meeting?

d) What is the probability that she is not late for either one (she is late for neither)?

e) What is the probability that she is not late for both meetings ?

f) Find the probability that she is late for the first meeting if she was late for the second meeting?

A Gallup Poll showed that 44% of Americans are satisfied with the way things are going in the United States. Suppose a sample of 25 Americans are selected.

Find the probability that no less than 7 Americans are satisfied with the way things are going.

Find the probability that exactly 15 Americans are not satisfied with the way things are going.

Find the probability that the number of Americans who are satisfied with the way things are going differs by greater than 2 from the mean.

Find the probability that greater than 7 Americans are satisfied with the way things are going.

Find the probability that at least 15 Americans are not satisfied with the way things are going.

Find the probability that no more than 9 Americans are satisfied with the way things are going.

Find the probability that more than 40% but at most 65% of these Americans are satisfied with the way things are going.

Round to 4 decimals.

In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet.† You work day shifts in a Honolulu hospital emergency room. At the beginning of each month you select your days off, and you pick 7 days at random in January to go surfing. Let r be the number of days the surf is at least 6 feet.

(a) Make a histogram of the probability distribution of r.

(b) What is the probability of getting 4 or more days when the surf is at least 6 feet? (Round your answer to three decimal places.)


(c) What is the probability of getting fewer than 2 days when the surf is at least 6 feet? (Round your answer to three decimal places.)


(d) What is the expected number of days when the surf will be at least 6 feet? (Round your answer to two decimal places.)
days

(e) What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
days

(f) Can you be fairly confident that the surf will be at least 6 feet high on one of your days off? Explain. (Round your answer to three decimal places.)

---Select--- Yes No , because the probability of at least 1 day with surf of at least 6 feet is  and the expected number of days when the surf will be at least 6 feet is  ---Select--- less than equal to greater than one.

Consider a circuit-switching scenario in which Ncs users, must share a link of capacity 150 Mbps. Each user alternates between periods of activity when the user generates data at a constant rate of 20 Mbps and periods of inactivity when he generates no data. Suppose further that he is active only 20% of the time. Assume a circuit switched TDM. What is the maximum number of circuit-switched users that can be supported? Assume packet switching is used for the remaining parts of this question. Suppose there are 13 packet- switching users (i.e., Nps = 13). Can this many users be supported under circuit-switching? Explain. What is the probability that a given (specific) user is transmitting, and the remaining users are not transmitting? What is the probability that one user (any one among the 13 users) is transmitting, and the remaining users are not transmitting? When one user is transmitting, what fraction of the link capacity will be used by this user? What is the probability that any 7 users (of the total 13 users) are transmitting and the remaining users are not transmitting? (Hint: you will need to use the binomial distribution.) What is the probability that more than 7 users are transmitting? Comment on what this implies about the number of users supportable under circuit switching and packet switching. What is the probability that more than 7 users are transmitting? Comment on what this implies about the number of users supportable under circuit switching and packet switching.

Recently you've noticed that with many products no longer obtainable through purchase at brick and mortar locations, your family is making more purchases on various ecommerce websites.

Define X to be a random variable denoting the total number of packages delivered to your house each day. The probability mass function (pmf) of X is as follows:

What is the probability you receive zero packages back to back days?

What is the probability you receive at most two packages?

Compute the expected number of packages received.

Compute the expected value of

Compute the expected value of standard deviation of X.