After the severe 2008 stock market crash, an increasing number of publicly traded firms announced stock buyback (repurchase) programs. Most analysts are also predicting that many firms will use the money saved due to the 2018 tax law which lowered highest corporate tax rate from 35% to 21% to repurchase their stock or pay dividends. Please explain what benefits or rationale, if any, firms see in stock repurchases and how would investors react to these repurchase programs. You would want to use your understanding of chapter 14 stock repurchase discussion in your answers

Make Excel do all calculations

An insurance company has found that 10% of its claims are for damages resulting from burglaries. A random sample of 20 claims is pulled.

a. What is the expected number(mean) that will be claimed for damages resulting from burglaries?

b. What is the standard deviation?

Use Excel function BINOMDIST (watch podcast) as appropriate in the following questions.

c. What is the probability that exactly 5 of the 20 will contain claims that are for burglary damages?

d. What is the probability that fewer than 5 will contain claims that are for burglary damages?

e. What is the probability that at least 5 will contain claims that are for burglary damages?

1) The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with mean of three cracks every five miles. What is the probability that there are exactly two cracks that require repair in 3 miles of highway?

2) The volume of a shampoo filled into a container is a continuous random variable uniformly distributed with 240 and 260 milliliters. What is the probability that the container is filled with MORE THAN the advertised target of 255 milliliters?

3) The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. What is the probability that you wait between 10 and 20 minutes for a taxi?

Play the following games in the Games Fair:

• Three Prize Roller
• Word Scramble
• Marble Draw
• Ten Spinner

For each Games Fair game, answer the following questions:

1. Create the probability distribution in a table for all the outcomes where X is the random variable representing the number of points awarded.
2. Communicate how you arrived at the probability of each outcome.
3. What is the expected value, E(X), for the game? You may include this in your table from the distribution. If the game costs 10 points to play, how much would the player expect to win or lose?
4. Create the bar graph for the Probability Distribution.

The distribution of the number of people in line at a grocery store checkout has a mean of 3 and a variance of 9. A sample of the numbers of people in 50 grocery store checkout lines is taken.

(a) (3 points) What’s the probability that the sample mean is less than 4.5? Round your answer to four (4) decimal places.

(b) (3 points) What’s the probability that the sample mean is more than 2.25? Round your answer to four (4) decimal places.

(c) (3 points) What’s the probability that the sample mean differs from the population mean by more than 0.75? Round your answer to four (4) decimal places.

The amount of milk that the American Cookie Company sells in a given week is random. Suppose the milk sells for $2.00 per cup and it costs the store $1.50 per cup. The following describes the distribution of demand for milk in a one week period. There is a probability of 0.14 that the store will sell 100 cups of milk; there is a probability of 0.2 that the store will sell 150 cups of milk; there is a probability of 0.34 that the store will sell 170 cups of milk; otherwise, the store will sell 220 cups of milk. What is the expected number of cups of milk the store will sell in a given week? (please express your answer using 2 decimal places)

Of 121 coins, one has a symbol on both sides, the others have a number on one side and a symbol on the other. Otherwise the coins cannot be
distinguish between them. After good mixing in a bag, one of the coins is pulled out
and threw it three times in a row. After each throw there is a symbol on top.

a)Then what is the probability that the coin with the two symbols was pulled?

b)How many times had to be thrown and symbol had to appear in each case, so that this probability is greater than 1/2 ?

(c) What is the probability that neither the coin with the two symbols is drawn nor three coins with symbols thrown?

A computer is shared by 2 users who send tasks to a computer remotely and work independently. At any minute, any connected user may disconnect with probability 0.5, and any disconnected user may connect with a new task with probability 0.2. Let X(t) be the number of concurrent users at time t (in minutes). This is a Markov chain with 3 states: 0, 1, and 2. The probability transition matrix can be calculated and it is Generate 10000 transitions of the Markov chain. What percent of times do you find your generated Markov chain in each of its 3 states? Write using R code.

- Introduce the City and State. Tell us the average number of days of precipitation in that city for the month of April. --> I chose Las Vegas NV where it rained 3 days,

Calculations

- What is the probability of having exactly 10 days of precipitation in the month of April?

- What is the probability of having less than 3 days of precipitation in the month of April?

- What is the probability of having more than 15 days of precipitation in the month of April?

Analysis

Write a sentence for each of the probabilities explaining what those probabilities mean in the context of days of precipitation in your chosen city.

Would any of the situations be considered unusual? Why or Why Not?