In class, we calculated the externality through tax revenues of educating a Binghamton student, assuming some parameter values (e.g. that combined state and local taxes are 12% of earnings). Your guess about those parameter values might be different from what we used in class. What’s your personal guess about the values of those parameters? Take your guess about those parameter values and calculate the size of the externality. Is the state’s subsidy of Binghamton students’ education larger or smaller than the externality through taxes? Do you think the externality through taxes is larger or smaller than the total externality?

Describe, in detail, what would happen if you fell into a black hole, from both your perspective, and the perspective of someone who is watching you fall in. You should include specific effects, including effects on space, time, and what you would see.

Do some research online and find 3 cars you are thinking of buying (ranging from low budget, to mid-budget, to one that is your dream car). Find their prices and how many miles per gallon they get

Car A: $26,793 28MPG

Car B: $39,735 17MPG

Car C: $161,139 13PMG

Suppose that you plan on using the car for 100,000 miles . Also let’s assume that all the cars have about the same overall cost of maintenance (just to simplify so you don't have to figure that into your calculations).

• The major uncertainty that you need to entertain is the price of gas in the future. You guess that there are roughly 4 options, given peak oil production and a tailing-off of global oil resources within the next 40 years (gas is a finite resource, in other words): 1) gas at $3 per gallon; 2) at $4; 3) at $5; 4) at $8. This is your partition, your states of affairs.

• The courses of action you may take are the three choices you have for your cars.

• The utilities you assign to your options are the respective price of each car plus the cost of gas for a “lifetime.”

a) Draw a table that lists the states of affairs across the top, and the choices/cars down the left side.

b) Work out the cost of gas for each car over its lifetime given the respective mpg, then fill in the utility of each choice (gas

plus cost of car) in each state of affairs. [40pts]

c) According to the table, is there an option that “dominates” the others? (Remember, in this example domination is about the lowest overall price.) In other words, is there a state of affairs in which one choice of car has costs lower than all the others AND in no other state of affairs does that choice of car cost more than any of the others? Briefly explain your answer and what that answer means.

d) Go back to the table you made in b). Attach the following probabilities to the gas prices over the lifetime of your car: 1) Pr($3)=50%; 2) Pr($4)=40%; 3) Pr($5)=8%; 4) Pr($8)=2%. Compute the expected value of each choice with these probability assignments, and then assess whether there is a value that dominates the others. Briefly explain your answer and what it means.

You decide to study the effect of GRE preparatory course on GRE score. Describe, in detail, how you will design your study, how you will collect data, and how you are going to statistically test whether the GRE course had an effect on GRE score. Be as specific as you can about your hypotheses. How would you, if at all, change your study if you decided to study the effect of the GRE preparatory course on graduate school admission instead?

Poisson

1. Passengers of the areas lines arrive at random and independently to the documentation section at the airport, the average frequency of arrivals is 1.0 passenger per minute.

to. What is the probability of non-arrivals in a one minute interval?

b. What is the probability that three or fewer passengers arrive at an interval of one minute?

C. What is the probability not arrived in a 30 second interval?

d. What is the probability that three or fewer passengers arrive in an interval of 30 seconds?

2. The average number of spots per yard of fabric follows a Poisson distribution. If λ = 0.2 spot per square yard.

to. Determine the probability of finding 3 spots in 2 square yards.

b. What is the probability of finding more than two spots in 4 square yards?

C. What is the average stain in 10 square yards?

Hypergeometric

1. It is known that of 1000 units of ACME cars of a lot of 8000, they are red. If 400 cars were sent to a wholesaler, what is the probability that you will receive a hundred or less red cars. (Assume X = red auto)

a) P (X <= 100) =? (Hypergeometric)

b) P (X> 50) =?

c) E (x) = expected value red cars

I. Continuous Distribution: Normal

1. Long distance telephone calls have a normal distribution with µ x = 8 minutes and σx = 2 minutes. Taking a unit up.

to. What is the probability that a call will last between 4 minutes and 10 minutes?

b. What is the probability that a call will last less than 9 minutes?

C. What is the value of X so that 12% of the experiment values ​​are greater than it?

d. If samples of size 64 are taken:

i. What proportion or probability of the sample means of the calls will be between 7 minutes and 9 minutes?

ii. What proportion or probability of the sample means of the calls is greater than 5 minutes?

iii. Between that two values ​​from the sample mean are 90% of the data.

Exponential

1. The time to fail in hours of a laser beam in a cytometric machina can be modeled by an exponential distribution with λ = .0005

to. What is the probability that a laser will fail more than 10000 hours?

b. What is the probability that a laser will fail less than 20,000 hours?

C. What is the probability that a laser will fail between 10,000 and 20,000 hours?

Lori, age 26, works as a waitress at an upscale restaurant in Dallas, Texas. After the restaurant closed one evening, she drove home in a blinding rainstorm. A drunk driver ran a red light, smashed head-on into Lori’s car, and was instantly killed. Lori was more fortunate. She lived but was unable to work for six months. During that time, she incurred medical bills in excess of $100,000 and lost about $20,000 in tips and wages. The restaurant did not provide any health or disability income insurance, whereas the driver had a life and health insurance plan.

Identify the major pure risks or pure loss exposures to which the drunk driver and Lori are exposed respectively with respect to each of the following. Explain your answer.

i) Personal loss exposures

ii) Property loss exposures

iii) Liability loss exposures

1. How and why does the CMBR, redshifts of distant galaxies, and relative abundances of the elements support a beginning to our universe?

2. About 380,000 years after the big bang, the universe became transparent to light. What had to occur for this to happen and what remnant is left behind that we can see today?

3. Go to Planck and The Cosmic Microwave Background and answer the following: How accurate is the the Planck data? What do the different colors help us know about the universe we see today?

4. How do we detect a red-shifted or blue-shifted galaxy? What is a "z" number and how is it calculated?

Which of the following is true about stockholders' equity?

a

This section of the Balance Sheet will always equal total assets.

b

This section of the Balance Sheet can only be increased if the company sells more stock to its stockholders.

c

Corporations always must have at least two accounts in this section of the Balance Sheet: common stock and retained earnings.

d

Retained earnings in stockholders equity is the one account on the Balance Sheet that the ending balance at the end of the period is zeroed out and does not carry over to the following period.

Prove the claim at the end of the section about the Euclidean Algorithm and Fibonacci numbers. Specifically, prove that if positive naturals a and b are each at most F(n), then the Euclidean Algorithm performs at most n − 2 divisions. (You may assume that n > 2.)

16) Unfortunately, arsenic occurs naturally in some ground water (Reference: Union Carbide Technical Report K/UR-1). A mean arsenic level of ? = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of ?̅ = 7.2 ppb arsenic, with ? = 1.9 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use ? = 0.01.

a) What is the level of significance? State the null and alternative hypotheses.

b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution of the sample test statistic.

c) Find (or estimate) the P-value.

d) Based on your answers in parts (a) through (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

e) Interpret your conclusion in the context of the application.