Consider a taxi stand where inter-arrival times of the taxis and the customers are both exponential with means of 0.5 and 1 minutes, respectively. Stand has 3 spots that taxis can park while waiting for the arriving customers. Arriving taxis leaves the stand when all the spots are occupied. Similarly, arriving customers are also lost when there is no taxi in the stand.

a. Model this system as a birth and death process by defining the state and the state space, and drawing the rate diagram.
b. Compute the steady-state probabilities.
c. What is the expected number of taxis waiting at the stand in the long run?

Consider a taxi stand where inter-arrival times of the taxis and the customers are both exponential with means of 0.5 and 1 minutes, respectively. Stand has 3 spots that taxis can park while waiting for the arriving customers. Arriving taxis leaves the stand when all the spots are occupied. Similarly, arriving customers are also lost when there is no taxi in the stand.

a. Model this system as a birth and death process by defining the state and the state space, and drawing the rate diagram.

b. Compute the steady-state probabilities.

c. What is the expected number of taxis waiting at the stand in the long run?

The table below contains a list of species and their abundances for two grassland communities around Serengeti National Park, Tanzania. Use the below data to answer the following question.

Using the Shannon diversity index, what is p_i for Sporobolus ioclados?

14. What are the highest tax rates for each of the following scenarios?

____. Operating income from a hotel earned by a foreign corporation (excluding branch profits tax)

____. Interest income earned by a foreign corporation from a US borrower

____. Net rental income earned by an U.S. individual (exclude the passthrough deduction)

____. Capital gain earned by an U.S. individual

____. Interest income earned by a U.S. corporation

____. Capital gain earned by an U.S. corporation

____. Depreciation recapture on the sale of U.S. real estate (Section 1250 property) for an individual

____. Depreciation recapture on the sale of U.S. real estate (Section 1245 property) for an individual

Using the demand and supply diagrams (one for each market), show what short-run changes in price and quantity would be expected in the following markets if terrorism-related worries about air safety cause travelers to shy away from air travel. Each graph should contain the original and new demand and supply curves, and the original and new equilibrium prices and quantities. For each market, write one sentence explaining why each curve shifts or does not shift.

The market for air travel.

The market for rail travel.

The market for hotel rooms in Hawaii.

The market for gasoline.

1. What, if anything, does each of the following quotations tell you about the demand elasticity? Explain.

a. "I drink two cups of coffee every morning regardless of the price."

b. "Attendance at the ball park went down when they increased the ticket price, but in spite of the decreased attendance, more money was taken in.”

c. "When the newspaper raised its price, the number of newspapers sold dropped by 20%.

d. My budget is $10 a week for cigarettes. I don’t care what happens to the price of cigarettes, once my budget is gone, I chew gum!

In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.62 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed."

Q: What is the minimum angular speed, in rpm, for which the ride is safe?

In an old-fashioned amusement park ride, passengers stand inside a 4.5-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.65 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed." What is the minimum angular speed, in rpm, for which the ride is safe?

On September 7​, the billing​ date, Verna had a balance due of ​$565.85 on her credit card. Assume that the interest rate is​ 1.1% per month. Suppose that​ Verna's bank uses the average daily balance method. Answer parts​ (a) through​ (d). Sept. 11 Payment ​$280.00 Sept. 23 ​Charge: Airline ticket ​$332.00 Sept. 24 ​Charge: Hotel bill ​$190.01 Oct. 2 ​Charge: Clothing ​$84.91 ​a) Determine​ Verna's average daily balance for the billing period from September 7 to October 7. The average daily balance for the billing period was ​$