You have four hard drives. Two of the drives have a failure rate of 1.75% (pf = 0.0175), and the other two have a failure rate of 2.5%. Assume that failures of the hard drives are independent events. (a) What is the probability of failure of your system? (b) Assuming that your quantities of 1.75% and 2.5% drives remain equal (that is, you have n 1.75% and n 2.5% drives), what is the minimum total number of hard drives your system would have to have to exceed a 50% failure rate?

(Note: failure of the system is defined to be the failure of one of the hard drives.)

Conduct the appropriate test of the specified probabilities using the given information. Use

α = 0.05.

The five categories are equally likely to occur, and the category counts are shown in the table

Given:

H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 1/5

H_a: At least one p_i is different from 1/5.

FInd:

Find the test statistic. (Round your answer to two decimal places.)

Χ² = ??

Find the rejection region. (Round your answer to two decimal places.)

Χ² > ??

Consider a locus with two alleles - B and b. B is dominant, while b is recessive. There is no mutation. B has a selective advantage relative to b, so that the fitnesses of the three genotypes are BB = 1, Bb = 1, and bb = 1-s. In this case, s = 0.50, so that bb homozygotes have 50% fitness of heterozygotes and BB homozygotes. If the population has the following genotypic counts prior to selection of BB = 500, Bb = 250, and bb = 250, what is the expected change in the frequency of B after one generation with selection? Please give your answer to two decimal places.

Moerdyk & Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the one with the higher IRR will also have the higher NPV, i.e., no conflict will exist.

Moerdyk & Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the one with the higher IRR will also have the higher NPV, i.e., no conflict will exist.

Assume two firms 1 and 2. The inverse market demand function is given by:             

P=30-(q₁+q₂)

Each firm produces with marginal costs of

MC = 6

Fixed costs are zero.

The next questions refer to the Cournot duopoly.

Question 1 (1 point)

What is Firm 1's total revenue function?

Question 1 options:

Question 2 (1 point)

What is Firm 1's marginal revenue function?

Question 2 options:

Question 3 (1 point)

What is Firm 1's response function?

Question 3 options:

Question 4 (1 point)

If Firm 1 thinks that Firm 2 chooses to supply q₂=10, then Firm 1's profit maximizing quantity would be q₁*=

Question 4 options:

Question 5 (1 point)

If Firm 2 thinks that Firm 1 chooses to supply q₁=7, then Firm 1's profit maximizing quantity would be q₁*=

Question 5 options:

Question 6 (1 point)

In equilibrium, each firm will supply q_i=

Question 6 options:

Question 7 (1 point)

The market price in equilibrium will be P*(q₁+q₂)=

Question 7 options:

Question 8 (1 point)

In equilibrium, each firm's total revenue is equal to TR_i=

Question 8 options:

Question 9 (1 point)

In equilibrium, each firm's total variable cost is TVC_i=

Question 9 options:

Question 10 (1 point)

In equilibrium, each firm's total profit is _i=

Question 10 options:

Question 11 (1 point)

In equilibrium, total consumer surplus is CS=

Question 11 options:

Suppose that a beachgoer uses two lenses from a pair of disassembled polarized sunglasses and places one on top of the other. What would he observe if he rotates one lens 90° with respect to the normal position of the other lens and looks through them directly at the sun overhead?

Group of answer choices

Light with an intensity that is the same of what it would be with one lens

Light with an intensity reduced to about 50% of what it would be with one lens

Complete darkness, since no light would be transmitted

Light with an intensity reduced to about 25% of what it would be with one lens

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.

(A) Conduct a test of independence to determine whether hours of sleep are independent of age.

State the null and alternative hypotheses.

H₀: Hours of sleep per night is independent of age.
H_a: Hours of sleep per night is not independent of age. CORRECT!

Find the value of the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

Using a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We cannot conclude that hours of sleep per night and age are not independent. CORRECT!

(B)

What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Fewer than 6    %

6 to 6.9 %

7 to 7.9 %

8 or more %

Agenda Item #5: The Spread Network L.L.C. Story. – Capital Budgeting

Speed of information has always played a key role in history, and this also applies equally to financial markets. Legend has it, that in 1815 Nathan Rothschild was able to exploit the early information he received (by way of pigeon it is said) of the victory against Napoleon at Waterloo to make a tidy sum. A few ₤100,000 when the average annual salary was just ₤50. Fast-track 184 years to 2009, and the Spread Network has concocted a plan to build the first and fastest, dedicated fibre optic route between two stock exchanges[1].  It plans to connect the Chicago Mercantile Exchange with the NASDAQ exchange in New Jersey, roughly 1400 km’s one way or 2800km return trip. It will require signal boosters every 100 km or so. To elaborate on ‘speed’, they aimed to reduce the time it took to submit a purchase order (offer) for financial assets (like shares), and receive confirmation of the offer price (acceptance of offer), from 14.65 milliseconds to 12.9 milliseconds[2]. About 1/10th of the time it takes to blink. This was unprecedented at the time, and it was hoped that by shaving around 1 and a half thousandths of a second off the travel time it could be leased to high frequency traders and investment banks for millions of dollars per month.

You snagged an internship at J.P. Morgan investment bank within the corporate finance division, and it is up to you to determine the viability of this project. So, what is speed worth?

The project will last for 8 years, beginning in 2011 (year 0) and ending in 2019 (year 8). Depreciation is straight line to zero, and taxation (at the time) is 35% in the United States. In any year with a negative EBIT, there is no tax. The capital investment for the fibre line project is $350,000,000 (invested in year 0), including costs of amplification sites, earthmoving equipment, easements etc. Working capital is expected to be $60,000,000, returned at the end of the project. A 24 hours a day, 7 days a week maintenance team is required to ensure 99.99% operational capacity, costing $60 million per year, and increasing at 3% per year. The project success hinges on access to the fibre ports in the exchanges, they know this and charge $50,000,000 per year (combined), declining by 5% p.a. as demand declines.          A team of surveyors and builders who inspected the 1400 km path cost $1.5 million. At the end of the project, the technology is obsolete for its purpose in investment banking, but it can be sold to a telecom provider (contributing to the revenue for year 8) for $127,000,000. Revenue is subscription based at $3,600,000 per year, per subscription. In year 1 there will be 200 subscriptions, year 2 is 150, year 3 is 100, year 4 is 50. In year 5, 6, 7, 8 only 20 subscriptions are taken in per year. The all-important discount rate is 14.5%.

Your manager’s guidance: In addition to presenting the NPV and IRR (and associated advice), your manager likes to scope out as many dimensions of a potential business decision as possible before providing the report. They might like to know how changes to revenues or costs might affect the viability of the project, including how this may impact the NPV and IRR. Another factor is the sensitivity of the cost of capital. Ensure your spreadsheet can cope with changes to these variables on the fly.

Two television stations compete with each other for viewing audience. Local programming options for the 5:00 P.M. weekday time slot include a sitcom rerun, an early news program, or a home improvement show. Each station has the same programming options and must make its preseason program selection before knowing what the other television station will do. The viewing audience gains in thousands of viewers for Station A are shown in the payoff table.

Determine the optimal strategy for each station. Round your answers to two decimal places. If your answer is zero, enter zero "0".

The optimal strategy is for Station A to implement:

strategy a₁ with probability ?

strategy a₂ with probability ?

strategy a₃ with probability ?

The optimal strategy is for Station B to implement:

strategy b₁ with probability ?

strategy b₂ with probability ?  

strategy b₃ with probability ?

What is the value of the game? Round your answer to two decimal places.

The value of the game =

Note:Please show how to solve for probability value for a1, a2, a3, b1, b2, b3, and the value of the game.