A second-hand car dealer is doing a promotion of a certain model of used truck. Due to differences in the care with which the owners used their cars, there are four possible quality levels (q1 > q2 > q3 > q4) of the trucks on sale. Suppose that the dealer knows the car’s quality (quite obvious), but buyers only know that cars for sale can be of quality q1, q2, q3 or q4. Faced with a given car, the buyers cannot identify its precise quality. However, they believe that there is a probability 0.2 that the quality is q1, a probability 0.3 that it is q2, and a probability 0.3 that it is q3. The respective values of the cars to the buyers are $20,000 for the q1 quality, $15,000 for q2, $10,000 for q3 and $5,000 for q4.

Assume that all agents (including the buyers) are risk neutral (only care about “return”) in the sense that a buyer does not want to pay more for a car than its expected worth and the car owner (the car dealer) does not wish to sell at less than what the car is worth.

a) Define adverse selection in general and in the current context.

b) If all four types of used truck are offered for sale, what is the highest price a buyer would be willing to pay for a used truck? At this price, what type(s) of truck will be offered for sale?

c) Now suppose the $20,000 trucks are no longer offered for sale but other types are (and is known to the buyers). What is the maximum price a buyer is willing to pay for a used truck? At this price, what type(s) of truck will be offered for sale? [Hint: What are the respective probabilities of the types of cars that will be offered for sale?]

d) Explain how adverse selection causes this market to a partial market breakdown (i.e., only the worst used trucks (q4 type) are traded in the market).

Nate and Gabriel are two friends who say they have no previous knowledge of statistics. They are going to take a placement test to see if they should start at the introductory level or not.

The placement test is a multiple-choice test with 85 questions. Each question has 4 multiple-choice options with exactly one correct answer.

What is the expected number (mean) of correct answers if a student were to randomly guess?  (Do not round)

What is the standard deviation for the number of correct answers if a student were to randomly guess?  (Round to two decimal places)

The usual number of correct answers, if a student were to randomly guess, would be  to  . (Round to the nearest whole number that would be within the interval.)

What is the probability of getting 24 or more questions correct if you are randomly guessing?  (Round to four decimal places.)

What is the probability of getting 53 or more questions correct if you are randomly guessing?  (Round to four decimal places.)

Nate got 24 questions correct.

Gabriel got 53 questions correct.

Is it reasonable to believe that Nate had no prior knowledge of statistics?

• yes
• no

Why or why not?

Is it reasonable to believe that Gabriel had no prior knowledge of statistics?

• yes
• no

Why or why not?

For this problem, use the fact that the expected value of an event is a probability weighted? average, the sum of each probable outcome multiplied by the probability of the event occurring. You own a house worth $400,000 that is located on a river. If the river floods? moderately, the house will be completely destroyed. This happens about once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, which only happens about once every 100 years. What would be the annual premium without a seawall for an insurance policy that offers full? insurance? Without a seawall, the annual premium is ?$ . ?(Round your response to the nearest whole? number.) $8,000 What would be the annual premium with a seawall for an insurance policy that offers full? insurance? With a seawall, the annual premium is ?$ . ?(Round your response to the nearest whole? number.)$4,000

For a policy that only pays 80?% of the home? value, what are your expected costs without a? seawall?

Without a? seawall, the expected cost is ??? (Round your response to the nearest whole? number.)

For a policy that only pays 80?% of the home? value, what are your expected costs with a? seawall? With a? seawall, the expected cost is ??? ?(Round your response to the nearest whole? number.)

Give the named probability distribution for each of the following random variables with specific parameter values. You should name the parameters, that is, write the parameter name in your answer (for example, Binomial(n=30,p=0.5))

a) One of Nia’s cat meows when he wants petting. Assuming that the meows are independent of each other and the probability that a meow results in petting is 0.7, what is the distribution of Y: the number of meows until Nia pets him?

(b) Nia has 6 cats. Each cat has a 25% chance of finishing their dinner. The cats eat independently of each other. What is the distribution of X: the total number of cats that finish their dinner?

(c) Nia has a cat that meows a lot. The meows are independent and she meows on average 2 times per minute. What is the distribution of N: number of times this cat meows in half an hour?

(d) There are 30 options of cat toys in a pet store; however, out of those 30, Nia’s cats will only like 4 of them. Nia randomly chooses 2 toys at random and buys them for her cats. What is the distribution of W: the number of toys Nia bought that her cats will like?

Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are the specialty of his shop. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand, he estimates demand for cookies as

Each dozen sells for $0.69 and costs $0.46, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.29 and sold the following day as day-old merchandise.

a. Compute the expected profit or loss for each cookie making decision quantity. (Round your answer to the nearest whole number. Enter expected losses with a negative sign.)

b. Based on your answers to part a., what is the optimal number of cookies to make?

c. By using marginal analysis, what is the optimal number of cookies to make?

What is a narrative or doing in the body a Streptococcus pneumoniae bacteria. How did it you get into the body? In other words, how did the body inherit you. How do you move through the body? What path of destruction are you on? How will you wage battle against the body? How do you plan to win that battle? What will the body try to do to stop you? How will you fight back? Who wins?

Question 1
Neelo Mbiganyi received a notice of assessment from Botswana Unified Revenue Service (BURS) and the Commissioner General had
disallowed some of the expenditures that she had claimed. Discuss the appeals and objection processes that Neelo can follow explaining in detail the rights and obligations that both Neelo and the Commissioner General have in these processes. In your answer, also explain what the Commissioner General should do suppose Neelo wins the case.

1. What element is represented by the electron configuration 1s2 2s2 2p6 3s2 3p2 ? ____________

2. What element is represented by the orbital diagram: _____________

3. Draw the orbital diagrams (box/line notation) for the following species:

Mn2+ ____________________________________________

Cu ____________________________________________

4. Write the electron configuration for the following elements and ions using spdf notation (without noble gas abbreviations):

Cr ____________________________________________

Si ____________________________________________

Fe2+ ____________________________________________

P 3- ____________________________________________

5. Write the electron configuration for the following elements and ions using noble gas spdf notation: Sn2+ Br‾

6. What are the possible values of the angular momentum quantum number (l) when n = 4 ?

7. What are the possible values for the magnetic quantum number (ml ) when l = 2 ?

8. In the ground state of selenium, how many electrons share the quantum number: a) n = 4 _____________ b) l = 2 ______________ 1s 2s 2p 3s

9. List all the quantum numbers for each of the 9 electrons in fluorine. n l ml ms

a.

b.

c.

d.

e.

f.

g.

h.

i.

10. What are the possible quantum numbers for the last electron in zinc? n = ___________ l = ___________ ml = __________ ms = ___________

11. Which element has the largest atomic radius? a) Na or Li b) Zr or La or Sb or S

12. Which element has the smallest ionic radius? a) Na+ or Mg2+ b) Be2+ or O2- or F‾ or S2-

13. Which element has the highest ionization energy? a) Sr or Ba b) Br or I or Te

14. Which element has the greatest electron affinity (most negative ∆E)? a) Na or Cl b) Sr or Ba

15. Which alkaline earth metal has the smallest atomic radius? __________________

16. Which alkali metal has the highest ionization energy? __________________

17. Which halogen has the lowest electron affinity? __________________

1. Consider the following game. Owen and Carter both write $1 or $3 on a piece of paper simultaneously. If both write the same amount, Owen wins and gets the amount written. If players write different amounts, Carter wins and gets $2. The loser gets nothing. Which of the following is true?

Group of answer choices

A- Owen has a dominant strategy.

B-There is no pure strategy Nash equilibrium.

C-In a Nash equilibrium, Owen writes $3.

D-Carter has a dominant strategy.

Consider the following scenario.

Suppose there are 2 seats on the bus, X and Y. Nathan and Benjamin each choose one seat. Both prefer seat X. Nathan chooses first. Benjamin chooses after observing Nathan’s choice. If both choose the same seat, Nathan cannot sit. Both prefer sitting to not sitting.

In the scenario above, which of the following is true?

Group of answer choices

A-There is no pure strategy Nash equilibrium.

B-Nathan chooses seat X in any Nash equilibrium.

C-Nathan chooses seat Y in any Nash equilibrium.

D-Nathan can choose seat X or Y depending on the Nash equilibrium.

betting theory on tennis

A bookmaker has quoted odds on a tennis match between players I and II. The match consists of the best two out of three sets, i.e., if a player wins the first two sets, the third set is not played and the bet on it is canceled. The bookmaker is giving odds of 5 to 2 that player I will win the match and odds of 3 to 2 that player I will win each set. A bettor has 100 dollars which he can distribute by betting on either player I or II to win the match and any of the sets. All bets are made before the match starts (if there are only two sets, all bets on the third set are returned to the bettor).
(a) Find a way of placing bets so that no matter what happens the bettor is assured of winning an amount z where z is as large as possible. Formulate this problem as a linear programming and solve it using AMPL.
(b) What if now we have best three out of five sets, i.e., once a player wins three sets, no more sets are played and their corresponding bets are canceled, and everything else keeps the same? Re-solve the problem and compare the answer with part (a).