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> A manufacturer of electroluminescent lamps knows that the amount of luminescent ink deposited on one of its products is normally distributed with a mean of 1.2 grams and a standard deviation of 0.03 gram. Any lamp with less than 1.14 grams of luminescent

> Consider the joint distribution in Exercise 5.1.4. Determine the following: a. fY | 3(y) b. E(Y | X = 3) c. V(Y | X = 3)

> Consider the joint distribution in Exercise 5.1.1. Determine the following: a. Conditional probability distribution of Y given that X = 1.5 b. Conditional probability distribution of X that Y = 2 c. E(Y | X = 1.5) d. Are X and Y independent?

> Given the probability density function f (x) = 0.013x2e−0.01x/Γ(3), determine the mean and variance of the distribution.

> The conditional probability distribution of Y given X = x is fY|x(y) = xe−xy for y > 0, and the marginal probability distribution of X is a continuous uniform distribution over 0 to 10. a. Graph fY|x(y) = xe−xy for y > 0 for several values of x. Determin

> Thewaiting time for service at a hospital emergency department (in hours) follows a distribution with probability density function f (x) = 0.5 exp(−0.5x) for 0 < x.Determine the following: a. P(X < 0.5) b. P(X > 2) c. Value x (in hours) exceeded with pr

> The probability density function of the length of a metal rod is f (x) = 2 for 2.3 < x < 2.8 meters. a. If the specifications for this process are from 2.25 to 2.75 meters, what proportion of rods fail to meet the specifications? b. Assume that the proba

> The distance between major cracks in a highway follows an exponential distribution with a mean of 5 miles. a. What is the probability that there are no major cracks in a 10-mile stretch of the highway? b. What is the probability that there are two major

> The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. a. What is the probability that you wait longer than 1 hour for a taxi? b. Suppose that you have already been waiting for 1 hour for a taxi.

> The number of stork sightings on a route in South Carolina follows a Poisson process with a mean of 2.3 per year. a. What is the mean time between sightings? b. What is the probability that there are no sightings within three months (0.25 years)? c. What

> The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 15 minutes. a. What is the probability that there are no calls within a 30-minute interval? b. What is the probability that at least one c

> The life of automobile voltage regulators has an exponential distribution with a mean life of 6 years. You purchase a 6-year-old automobile with a working voltage regulator and plan to own it for 6 years. a. What is the probability that the voltage regul

> Suppose that the log-ons to a computer network follow a Poisson process with an average of three counts per minute. a. What is the mean time between counts? b. What is the standard deviation of the time between counts? c. Determine x such that the probab

> Suppose that X has an exponential distribution with a mean of 10. Determine the following: a. P(X < 5) b. P(X < 15 | X > 10) c. Compare the results in parts (a) and (b) and comment on the role of the lack of memory property.

> The total service time of a multistep manufacturing operation has a gamma distribution with mean 18 minutes and standard deviation 6. a. Determine the parameters λ and r of the distribution. b. Assume that each step has the same distribution for service

> Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c. P(X < 30) d. Find the value of x such that P(X < x) = 0.95.

> An article in Vaccine [“Modeling the Effects of Influenza Vaccination of Health Care Workers in Hospital Departments” (2009, Vol. 27(44), pp. 6261–6267)] considered the immunization of healthcare workers to reduce the hazard rate of influenza virus infec

> An article in Ad Hoc Networks [“Underwater Acoustic Sensor Networks: Target Size Detection and Performance Analysis” (2009, Vol. 7(4), pp. 803–808)] discussed an underwater acoustic sensor network to monitor a given area in an ocean. The network does not

> An article in the Journal of the National Cancer Institute [“Breast Cancer Screening Policies in Developing Countries: A Cost-Effectiveness Analysis for India” (2008, Vol. 100(18), pp. 1290–1300)] presented a screening analysis model of breast cancer bas

> The length of stay at a specific emergency department in a hospital in Phoenix, Arizona, had a mean of 4.6 hours. Assume that the length of stay is exponentially distributed. a. What is the standard deviation of the length of stay? b. What is the probabi

> Suppose that the construction of a solar power station is initiated. The project’s completion time has not been set due to uncertainties in financial resources. The completion time for the first phase is modeled with a beta distribution and the minimum,

> An allele is an alternate form of a gene, and the proportion of alleles in a population is of interest in genetics. An article in BMC Genetics [“Calculating Expected DNA Remnants from Ancient Founding Events in Human Population Genetics” (2008, Vol. 9, p

> The maximum time to complete a task in a project is 2.5 days. Suppose that the completion time as a proportion of this maximum is a beta random variable with α = 2 and β = 3. What is the probability that the task requires more than two days to complete?

> The length of stay at a hospital emergency department is the sum of the waiting and service times. Let X denote the proportion of time spent waiting and assume a beta distribution with α = 10 and β = 1. Determine the following: a. P(X > 0.9) b. P(X < 0.5

> European standard value for a low-emission window glazing uses 0.59 as the proportion of solar energy that enters a room. Suppose that the distribution of the proportion of solar energy that enters a room is a beta random variable. a. Calculate the mode,

> Use the properties of the gamma function to evaluate the following: a. Γ(6) b. Γ(5/2) c. Γ(9/2)

> Suppose that X has a beta distribution with parameters α = 2.5 and β = 2.5. Sketch an approximate graph of the probability density function. Is the density symmetric?

> Suppose that x has a beta distribution with parameters α = 2.5 and β = 1. Determine the following: a. P(X < 0.25) b. P(0.25 < X < 0.75) c. Mean and variance

> If the random variable X has an exponential distribution with mean θ, determine the following: a. P(X > θ) b. P(X > 2θ) c. P(X > 3θ) d. How do the results depend on θ?

> Derive the formula for the mean and variance of an exponential random variable.

> The time between calls to a corporate office is exponentially distributed with a mean of 10 minutes. a. What is the probability that there are more than three calls in one-half hour? b. What is the probability that there are no calls within one-half hour

> The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. a. What is the probability that more than three aircraft arrive within an hour? b. If 30 separate one-hour intervals are chosen, what is

> According to results from the analysis of chocolate bars in Chapter 3, the mean number of insect fragments was 14.4 in 225 grams. Assume that the number of fragments follows a Poisson distribution. a. What is the mean number of grams of chocolate until a

> Powermeters enable cyclists to obtain power measurements nearly continuously. The meters also calculate the average power generated over a time interval. Professional riders can generate 6.6 watts per kilogram of body weight for extended periods of time.

> Derive the probability density function for a lognormal random variable Y from the relationship that Y = exp(W) for a normal random variable W with mean θ and variance ω2.

> An article in Mathematical Biosciences [“Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients” (1998, Vol. 152(2), pp. 143–163)] considered the time delay between the initial infection by immunodeficiency virus type 1 (HIV-1

> A random variable X has the Poisson distribution a. Show that the moment-generating function is b. Use MX(t) to find the mean and variance of the Poisson random variable.

> Jennifer Olde calls you requesting an explanation of the fact-finding determination of a Federal Court of Appeals. Prepare a letter to be sent to Jenni fer answering this query. Her address is 3246 Highland Dri ve, Clifton, VA 20124.

> Interpret each of the following citations. a. Temp.Reg.§ 1.707-5T(a)(2). b. Rev.Rul. (l()-11, 1960-1 C.B. 174 c. TAM 8837003.

> Where can a researcher find newly issued Proposed, final, and Temporary Regulations?

> Why are certain Code Section numbers missing from the Internal Revenue Code (e.g., §§ 6, 7, 8, 9. 10)?

> Is § 212(1) a proper Code Section citation? Why or why not?

> Determine the subparts of§ 1563(a)(l ) (A).

> If a tax bill is vetoed by the President, the provisions cannot become law. Evaluate this statement.

> Federal tax legislation generally originates in the Senate Finance Committee. Comment on the validity of this statement.

> Explain the continuity of interest concept.

> List some tax provisions used to deter affluent taxpayers from obtaining preferential tax treatment.

> In general, what is the limitation on the deductibility of business interest expense? What happens to any business interest deduction disallowed under the limitation?

> Contrast the tax treatment between a community property state and a common law state.

> Aqua Corporation purchases nonresidential real property on May 8, 2015, for $1 million. Straight-line cost recovery is taken in the amount of $89,765 before the property is sold on November 30, 2018, for $1.5 million. a. Compute the amount of Aqua's reco

> Diego transfers real estate with an adjusted basis of $260,000 and fair market value of $350,000 to a newly formed corporation in exchange for 100% of the stock. The corporation assumes the liability on the transferred real estate in the amount of $300,0

> Fargo Corporation distributes property (basis of $260,000 and fair market value of $310,000) to a shareholder. Fargo Corporation has sufficient E & P for its distributions. What are the tax consequences of this distribution to Fargo?

> Henry, a freelance driver, finds passengers using various platforms such as Uber and Grubhub. He is single and has no other sources of income. In 2018, Henry's net income from driving is S61,000. Con1pute Henry's QBI Deduction and his tax liability.

> Jason and Paula are married. They file a joint return for 2018 on which they report taxable income before the QBI deduction of $200,000. Jason operates a sole proprietorship, and Paula is a partner in the PQRS Partnership. Both are a qualified trade or b

> Thad, a single taxpayer, has taxable income before the QBI deduction of $187,500. Thad, a CPA, operates an accounting practice as a single member LLC (which he reports as a sole proprietorship). During 2018, his proprietorship reports net income of $150,

> Maria and Javier are the equal partners in Maria, a partnership that is a qualifying trade or business. In the current year, Maria had $350,000 of ordinary income after reporting $500,000 in guaranteed payments to Maria and Javier for their services to M

> Robert is the sole shareholder and CEO of ABC, Inc., an S corporation that is a qualified trade or business. During the current year, ABC has net income of$325,000 after deducting Robert's Sl 00,000 salary. In addition to his compensation, ABC pays Rober

> Orion Corporation's board of directors decides to distribute property to its shareholders rather than pay a cash dividend. Why might Orion's board make this decision?

> Charlotte is a partner in, and sales manager for, CD Partners, a domestic business that is not a "specified services" business. During the tax year, she receives guaranteed payments of $250,000 from CD Partners for her services to the partnership as its

> Hummingbird Corporation, a closely held C corporation that is not a PSC, has $40,000 of net active income, $15,000 of portfolio income, and a $45,000 loss from a passive activity. Compute Hummingbird's taxable income for the year.

> Goose Corporation, a C corporation, incurs a net capital loss of $12,000 for 2018. I t also has ordinary income of $10,000 in 2018. Goose had net capital gains of $2,500 in 2014 and S5,000 in 2017. a. Determine the amount, if any, of the net capital loss

> Crane and Loon Corporations, two unrelated calendar year C corporations, have the following transactions for the current year. a. Compute the dividends received deduction for Crane Corporation. b. Compute the dividends received deduction for Loon Corpo

> Compute the charitable contribution deduction (ignoring the percentage limitation) for each of the following C corporations. a. Amber Corporation donated inventory of clothing (basis of $24,000, fair market value of $30,000) to a qualified charitable org

> Several years ago, Minjun, who is single, acquired§ 1244 stock in Blue Corporation at a cost of $60,000. He sells the Blue stock for $5,000 in the current year. Determine the amount and nature of Minjun's gain or loss recognized this year.

> In the current year, Nighthawk Corporation, a calendar year C corporation, has $3.7 million of adjusted taxable income, S 125,000 of business interest income, zero floor plan financing interest, and $1.4 million of business interest expense. a. Assume th

> Interpret each of the following citations. a. 54 T.C. 1514 (1970) b. 408 F.2d 1117 (CA-2, 1969) . c. 69-1 USTC ¶ 9319 (CA-2, 1969). d. 23 AFTR 2d 69-1090 (CA-2, 1969). e. 293 F.Supp. 1129 (D.Ct. Miss., 1967). f. 67-1 USTC ¶ 9253 (D.Ct. Miss., 1967). g. 1

> Benny sells property basis of $70,000) to Jet Corporation for $100,000. Based on the following conditions, how could the IRS challenge this transaction? a. Benny is the sole shareholder of Jet Corporation. b. Benny is the son of the sole shareholder of J

> Assume the same facts as in Problem 31, except that Susan's business reports net income of $150,000 (all of which is qualified business income). What is Susan's QBI deduction? Problem 31: Susan, a single taxpayer, owns and operates a bakery (as a sole p

> Assume the same facts as in Question 6, except that property is distributed. What factors must be considered when determining how the distribution is treated for tax purposes by Orange Corporation?

> Assume the same facts as in Problem 35, except that the business is a "specified services" business (e.g., a consulting firm) owned equally by Elliot and Conrad (an unrelated individual) in a two-member LLC. Assume that each member's share of net income,

> Susan, a single taxpayer, owns and operates a bakery (as a sole proprietorship). The business is not a "specified services" business. In 2018, the business pays $100,000 in W-2 wages, has $150,000 of qualified property, and has $350,000 in net income (al

> Troy Kennedy (1635 Maple Street, Syracuse, NY 13201) exchanges property (basis of $200,000 and fair market value of $850,000) for 75% of the stock of Red Corporation. The other 25% is owned by Sarah Mitchell, who acquired her stock several years ago. You

> Stella Watters is a CPA and operates her own accounting firm (Watters CPA LLC). As a single member LLC, Stella reports her accounting firm operations as a sole proprietor. Stella has QBI from her accounting firm of $540,000, she reports W-2 wages of $156

> Benton Company (BC), a calendar year entity, has one owner, who is in the 37% Federal income tax bracket (any net capital gains or dividends would be taxed at a 20% rate). BC's gross income is $395,000, and it5 ordinary trade or business deductions are $

> Assume the same facts as in Problem 31, except that Susan's business pays $60,000 of W-2 wages and reports net income of $200,000 (all of which is qualified business income). Susan also has a part-time job earning wages of $14,000 and receives $3,000 of

> Assume the same facts as in Problem 29, except that Tammy does not have a part-time job at BigCo. How, does this affect her qualified business income deduction?

> Tammy, a single taxpayer, has a part-time job at BigCo, a company in which she has no ownership interest. In addition, she owns and operates LittleCo, a sole proprietorship that is a qualified trade or business. Tammy is paid wages of $40,000 by BigCo an

> To which U.S. Court of Appeals would a person living in each of the following states appeal from the U.S. Tax Court' a. Texas. b. Colorado. c. Georgia. d. Montana. e. New York.

> In January of the current year, Don and Steve each invested $100,000 cash to form a corporation to conduct business as a retail golf equipment store. On January 5, they paid Bill, an attorney, to draft the corporate charter, file the necessary forms with

> In the current year, Jeanette, an individual in the 24% marginal tax bracket, recognized a $20,000 long-term capital gain. Also in the current year, Parrot Corporation, a calendar year C corporation, recognized a $20,000 Jong-term capital gain. Neither t

> Explain what is meant by the following citations. a. Rev.Proc. 2001-10, 2001-1 C.B. 272. b. Rev.Rul. 2011-14, 201 1-27 I.R.B. 31. c. Ltr.Rul. 201125030.

> In the current year, Pelican, Inc., incurs $50,000 of nondeductible fines and penalties. Its depreciation expense is $245,000 for financial statement purposes and $310,000 for tax purposes. How is this information reported on Schedule M-3?

> In the current year, Pelican, Inc., a calendar year C corporation, incurs $l0,000 of meals and entertainment expenses that it deducts in computing net income per the corporation's financial statements. All of the meals and entertainment expenditures are

> Using the legend provided, classify the overall objective of the particular tax provision. a. Like-kind exchange treatment. b. An increase in the individual tax rate. c. The S corporation election. d. Adoption expense credit. e. Percentage depletion. f

> Juniper, Inc., exchanges some real estate (basis of $800,000 and fair market value of $1 million) for other real estate owned by Birch, Inc., (basis of $1.2 million and fair market value of $900,000) and $100,000 in cash. The real estate involved is unim

> Elliot operates his clothing store as a single member LLC (which he reports as a sole proprietorship). In 2018, his proprietorship generates net income of $280,000, he pays W-2 wages of S 170,000, and he has qualified business property of $140,000. Ellio

> Grouse Corporation, a calendar year C corporation, had taxable income of $1.4 million, $1.2 million, and $700,000 for 2016, 2017, and 2018, respectively. Grouse has taxable income of $1.6 million for 2019. What are Grouse Corporation's minimum required e

> Jennifer is a CPA and a single taxpayer using the standard deduction. In 2018, her CPA practice generates net income of $162,000 and she has no other income or losses. Jennifer's taxable income before the QBI deduction is 150,000 ($162,000 - $12,000 stan

> Your client, Heron Corporation, has a deficit in accumulated E & P $300,000. Starting this year, it expects to generate annual E & P of $150,000 for the next four years and would like to distribute this amount to its shareholders. How should Heron Corpor

> Using the legend provided, classify each of the following tax sources. a. Sixteenth Amendment to the Constitution. b. Tax treaty between the United States and China. c. Temporary Regulations (issued 2015) . d. Revenue Procedure. e. An IRS publication.

> Locate the following cited items, and give a brief description of the topic or opinion in the item. a. § 6694(a). b. Reg.§ I.6694-I(b) c. Rev.Rul. 86-55, 1986-1 C.B. 373. d. PLR 8022027.

> Identify the name of the publisher for the following tax services. a. United States Tax Reporter. b. Standard Federal Tax Reporter. c. Federal Tax Coordinator 2d. d. Mertens Law of Federal Income Taxation. e. Tax Management Portfolios. f. CCH's Tax Resea

> Using the legend provided, classify each of the following citations as to the court. a. 388 F.2d 420 (CA-7, 1968). b. 79 T.C. 7 (1982) c. 54 S.Ct. 8 (USSC, 1933). d. 3 B.T.A. 1042 (1926) e. T.C.Memo 1954-141. f. 597 F.2d 760 (Ct.Cl., 1979). g. Ltr.Rul.

> Florence is the Chief Financial Officer of Hazel Corporation, a publicly traded, calendar year C corporation. For the current year, her compensation package consists of: How much of Florence's compensation is deductible by Hazel Corporation?

> Using the legend provided, classify each of the following citations as to the location. A citation may have more than one answer. a. &Acirc;&sect; 61(a)(13). b. Prop.Reg. &Acirc;&sect; I.368-2(b)(l) c. Rev.Pree. 77-37, 1977-2 C.B. 568. d. Temp.Reg.&Aci

> In 2018, Gray Corporation, a calendar year C corporation, has a $75,000 charitable contribution carryover from a gift made in 2013. Gray is contemplating a gift of land to a qualified charity in either 2018 or 2019. Gray purchased the land as an investme

> Answer the following questions. a. What are letter rulings? b. What are technical advice memoranda (TAMs)?

> Benny sells property basis of $70,000) to Jet Corporation for $100,000. Based on the following conditions, how could the IRS challenge this transaction? a. Benny is the sole shareholder of Jet Corporation. b. Benny is the son of the sole shareholder of J

> Cornflower Corporation distributes equipment (adjusted basis of $70,000, fair market value of $55,000) to its shareholder, Roy. Assume that Cornflower has more than $100,000 of current E & P. What are the tax consequences to Cornflower Corporation and to

> Heron Company purchases commercial realty on November 13, 2000, for $650,000. Straight-line depreciation of $287,492 is claimed before the property is sold on February 23, 2018, for $850,000. What are the tax consequences of the sale of realty if Heron i