All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
statistical techniques in business

Questions and Answers of Statistical Techniques in Business

16.3. Lax pair Consider the pair of first-order differential operators (called Lax pair):L(x, t | θ) = d dx+iβ4∂tφσ3 +msinhθ,cosβφ2σ1 +mcoshθ sinβφ2σ2 M(x, t | θ) = d
16.4. Derrick theorem The aim of this exercise is to show that the static solitonic solution of finite energy can only exist for 1+1 dimensional theories. Consider, in the (d +1) dimensional
16.5. Liouville theory and minimal modelsa. In the quantization scheme of the Sine–Gordon model in terms of the Liouville theory, determine the quantized values of the coupling constant g that
16.6. Conserved currents Using the algebra of the operators Dn and the null vector equation at the level 2 satisfied by 1,2 and 2,1, find the linear combination T6 of the basis vectors T(1)6 and
17.1. Causality and analiticity Consider a linear system in which the output b(t) depends on the input a(t) as b(t) = t−∞G(t −t) a(t) dt.If the system is causal, the Green function G(t
17.2. Decay process A particle of mass M and three-dimensional momentum P decays in two particles of masses m1 and m2.a. Use the conservation of the energy and the momentum to prove that the total
17.3. Physical region of the amplitudes Determine the physical region of the s-channel process when the mass of the particles are different.
17.4. Yang–Baxter equations Prove that the Yang–Baxter equations given in eqn. (17.3.52) of the text can be obtained as a consequence of the associativity condition of the Faddev–Zamolodchikov
17.5. Reflection amplitude Consider the following scattering amplitudes of a particle A and its anti-particle A| A(θ1)A(θ2) = S(θ) | A(θ2)A(θ1),| A(θ1)A(θ2) = t(θ) | A(θ2)A(θ1)+r(θ) |
17.6. Bootstrap equations Derive the bootstrap equations (17.4.68) imposing the commutativity of the processes shown in Figure (17.13).Hint. Note that the line of the particle Ai in the second graph
17.7. Scattering in a potential with two delta functions Consider a one-dimensional system of quantum mechanics with Hamiltonian given by H = p2 2m+V(x)with V(x) = −g1 δ(x+a)−g2 δ(x+a)(g1 and
17.8. Interpretation of the two-dimensional S-matrix.The non-relativistic S-matrix of a particle of mass m = 1 relative to the potential V(x) =−2aπδ(x) is given by˜S(k) = k+iπa k−iπa.If we
17.9. S-matrix with resonances.Consider an S-matrix for a neutral scalar particle.a. Show that the unitarity and crossing invariance equations S(θ)S(−θ) = 1, S(θ) = S(iπ −θ), imply that that
18.1. Bootstrap equations Prove that the most general solution of the bootstrap equation relative to a particle bound state of itself SAA(θ) = SAAθ − iπ3 SAAθ + iπ3is given by SAA(θ) =
18.2. Analytic structure of the S-matrix of the Bullogh–Dodd modela. Study the structure of the poles and zeros of the S-matrix of the Bullogh–Dodd model S(θ) = f23(θ) f−B3(θ) f B−2
18.3. Multiple poles Prove that the amplitude S11 of the fundamental particle cannot have higher-order poles by showing that the resonance angle of two heavier masses is larger than 2π/3. This makes
18.4. Double poles Use the values of the resonance angles of the S-matrix of the thermal TIM to explain the double poles that enter the amplitude S1,6 in terms of multi-scattering processes.
18.5. Non-relativistic scattering of distinguishable particles Consider the non-relativistic Hamiltonian H =− ∂2 x2ma−∂2 y2mb+2λδ(x−y) (18.12.33)and let χ(x,y) be its scattering
18.6. S-matrix of the Gross–Neveu model The Gross–Neveu model is a model of n-component neutral Fermi–field ψk(x); k =1, 2, . . . ,n (n ≥ 3) with four-fermion interaction L = i 2nk=1¯ψkγ
18.7. Integral representation Use the expansions 1coshx= 2∞k=0(−1)k e−(2k+1)x, 1 sinhx= 2∞k=0 e−(2k+1)x the infinite-product(α) (β)(α +γ ) (β −γ )=∞k=01+ γα +k1− γβ
18.8. Sine–Gordona. Study the analytic structure of the S-matrix of the solitons of the Sine–Gordon model, identifying all the sequences of the poles in the amplitudes.b. Using the following
18.9. Reflectionless points At ξ = π/n (n = 1, 2, . . .), the amplitude SR of the Sine–Gordon vanishes and the scattering of the soliton–anti-soliton reduces to a pure transmission. Use the
18.10. Bound states and semi-classical limit It can be proved that the renormalized coupling constantξ = β2 81 1− β2 8π.of the Sine–Gordon model comes from the quantum correction of the
18.11. Sine–Gordon and non-unitary modelsa. Find the value of ξ for which the S-matrix element S(1,1)(θ) of the Sine–Gordon model coincides with the S-matrix of the Yang–Lee model. Explain
19.1. Form factors of a free theory Consider the theory of a free bosonic field φ(x) associated to a particle A of mass m.a. Compute the form factors of φ(x) and prove that 0|φ(0)|A = 1/sqrt2.
19.2. Feynman gasa. Derive the equation of state of the Feynman gas associated to the form factors of the magnetization operators in the nearest-neighbour approximation. Prove that the pressure p(z)
19.3. Infinite products Using the integral dt te−βt sin2 αt 2= 1 4logα2 +β2β2 , and the identity satisfied by the functions(α)(β)(α +γ )(β −γ )=∞k=01+ γα +k1− γβ +k, to
19.4. Cluster properties Consider the form factors of a scattering theory based on the functions fx(θ) =tanh 12(θ +iπx)tanh 12(θ −iπx)that have the property limθ→∞fx(θ) = 1.a. Using the
19.5. Correlation functions of the Ising model Use the fermionic representation of the energy operator of the Ising model, = i ¯ ψψ, and the mode expansion of the fermionic field in terms of the
19.6. Form factors of the Yang–Lee model Using the form factors of the Sinh–Gordon model, obtain the form factors of the Yang–Lee by using the analytic continuation B→−23
20.1. Non-relativistic gas Consider a one-dimensional gas of N non-relativistic bosons on an interval of length L, with two-body repulsive interaction given by a delta-function. The Hamiltonian of
20.2. Simple TBA system Consider the TBA equations for a relativistic system made of one massive particle and with kernelϕ(θ) = 1 2πδ(θ).a. Solve explicitly the equation for the pseudo-energy
20.3. L-channel for Majorana fermions Consider the Dirac action of a Majorana massive fermion on a finite volume S = dt R2−R2 dx ¯ψ i γ μ ∂μ −m ψ.Quantize this system in the
21.1. Boundary States for a bosonic field Consider the two analytic and anti-analytic U(1) currents j(z) =n jnz−n−1 and¯j( ¯ z) =n¯jn ¯ z−n−1 related to a massless bosonic field ϕ(z,
21.2. Bogoliubov transformation and boundary state Consider a free massive scalar field ϕ(x, t) in (1+1) dimension with mass m = m− t < 0 m+ t ≥ 0.Therefore it admits two different mode
22.1. Tricritical Ising model with even perturbations Consider the TIM deformed by its even fields (x) (energy density field) and t(x)(vacancy density field) with conformal weights given by 2 =
23.1. Decay processes Consider the decay processes of the higher particles in the spectrum of 4 theory, Bk→rB1 +sB2 where r and s are all those integers which satisfy mk ≥ rm1 +sm2, r +s =
23.2. Short and long kinks Consider a simplified version of a potential with three vacua configurations, realized by the potential shown in the Figure below V(ϕ) = m2 2⎧⎨⎩(ϕ +2b)2, ϕ
23.3. Instantons Instantons are finite action classical solutions of Euclidean equations of motion and are closely related to tunnelling phenomena among degenerate vacua. Consider a unit-mass
24.1. Supersymmetric quantum mechanics Consider two quantum mechanics Hamiltonians H+ = −¯h2 2m d2ψdx2+V+(x), H− = −¯h2 2m d2ψdx2+V−(x).where the potential terms are obtained in terms of
24.2. Exponential behaviour of the fermionic zero mode The poles present in the Fourier transform of ψ(0)ab (x) are determined by the exponential behaviour at x→−∞of this function. This
24.3. Asymmetric well potential It is interesting to see what happens when the bosonic potential has two asymmetric wells| a and | b: in this case the asymptotic behaviours of the kink at x±∞are
In a General Social Survey, in response to the question“Do you believe in heaven?” 1127 people answered“yes” and 199 answered “no.”(a) Estimate the probability that a randomly selected
Software for statistical inference methods often sets the default probability of a correct inference to be 0.95.Suppose we make an inference about the population proportion of people who support
A recent GSS asked subjects whether they are a member of an environmental group and whether they would be very willing to pay much higher prices to protect the environment. Table 4.4 shows
Let y = number of languages in which a person is fluent. According to Statistics Canada, for residents of Canada y has probability distribution P(0) = 0.02, P(1) =0.81, and P(2) = 0.17, with
Let y denote the number of people known personally who were victims of homicide within the past 12 months. According to results from recent General Social Surveys, for a randomly chosen person in the
A ticket for a statewide lottery costs $1. With probability 0.0000001, you win a million dollars ($1,000,000), and with probability 0.9999999 you win nothing. Let y denote the winnings from buying
Let y be the outcome of selecting a single digit using a random number generator.(a) Construct the probability distribution for y. (This type of distribution is called a uniform distribution, because
For a normal distribution, find the probability that an observation falls (a) at least one standard deviation above the mean; (b) at least one standard deviation below the mean.
For a normal distribution, verify that the probability between(a) μ − σ and μ + σ equals 0.68.(b) μ − 1.96σ and μ + 1.96σ equals 0.95.(c) μ − 3σ and μ + 3σ equals 0.997.(d) μ −
Find the z-value for which the probability that a normal variable exceeds μ + zσ equals (a) 0.01, (b) 0.025,(c) 0.05, (d) 0.10, (e) 0.25, (f) 0.50.
Find the z-value such that for a normal distribution the interval from μ − zσ to μ + zσ contains (a) 50%,(b) 90%, (c) 95%, (d) 99% of the probability.
Find the z-values corresponding to the (a) 90th, (b)95th, (c) 99th percentiles of a normal distribution.
If z is the number such that the interval from μ−zσto μ+zσ contains 90% of a normal distribution, then explain why μ + zσ is the 95th percentile.
If z is the positive number such that the interval fromμ − zσ to μ + zσ contains 50% of a normal distribution, then(a) Which percentile is (i) μ + zσ? (ii) μ − zσ?(b) Find this value of
What proportion of a normal distribution falls(a) above a z-score of 2.10?(b) below a z-score of −2.10?(c) between z-scores of −2.10 and 2.10?
Find the z-score for the number that is less than only 1% of the values of a normal distribution.
Mensa is a society of high-IQ people whose members have a score on an IQ test at the 98th percentile or higher.(a) How many standard deviations above the mean is the 98th percentile?(b) For the
According to a recent Current Population Reports, self-employed individuals in the United States work an average of 45 hours per week, with a standard deviation of 15. If this variable is
The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in studies with high-risk infants. It has approximately a normal distribution with a mean
For a study in Aarhus University Hospital(Denmark), 5459 pregnant women who reported information on length of gestation until birth had mean=281.9 days and standard deviation = 11.4 days. A baby is
Suppose that the weekly use of gasoline for motor travel by adults in Canada is approximately normally distributed, with a mean of 16 gallons and a standard deviation of 5 gallons.(a) What proportion
On the midterm exam in introductory statistics, an instructor always gives a grade of B to students who score between 80 and 90. One year, the scores have approximately a normal distribution with
For a SAT distribution (μ = 500, σ = 100) and an ACT distribution (μ = 21, σ = 4.7), which score is relatively higher, SAT = 600 or ACT = 29? Explain.
Suppose that property taxes on homes in Iowa City, Iowa, have an approximately normal distribution with a mean of $4500 and a standard deviation of $1500. The property tax for one particular home is
An energy study in Gainesville, Florida, found that in March 2015, household use of electricity had a mean of 673 and a standard deviation of 556kWh (kilowatt-hours).(a) If the distribution were
Five students—the females Ann and Betty and the males Clint, Douglas, and Edward—are rated equally qualified for admission to law school, ahead of other applicants.However, all but two positions
Construct the sampling distribution of the sample proportion of heads, for flipping a balanced coin(a) Once.(b) Twice. (Hint: The possible samples are (H, H), (H, T),(T, H), (T, T).)(c) Three times.
The probability distribution associated with the outcome of rolling a balanced die has probability 1/6 attached to each integer, {1, 2, 3, 4, 5, 6}. Let (y1, y2) denote the outcomes for rolling the
An exit poll of 1126 voters in the 2014 New York gubernatorial election indicated that 55% voted for the Democratic candidate, Andrew Cuomo, with most of the rest voting for the Republican candidate,
According to Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 13.6 and a standard deviation of
Refer to Exercise 4.6.The mean and standard deviation of the probability distribution for the lottery winnings y are μ = 0.10 and σ = 316.23.Suppose you play the lottery 1 million times. Let ¯y
According to a General Social Survey, in the United States the distribution of y = number of good friends (not including family members) has a mean of 5.5 and a standard deviation of 3.9.Suppose
The scores on the Psychomotor Development Index(PDI), a scale of infant development, are approximately normal with mean 100 and standard deviation 15.(a) An infant is selected at random. Find the
A study plans to sample randomly 100 government records of farms in Ontario to estimate the mean acreage of farms in that province. Results from an earlier study suggest that 200 acres is a
According to the U.S. Census Bureau, the number of people in a household has a mean of 2.6 and a standard deviation of 1.5.Suppose the Census Bureau instead had estimated this mean using a random
At a university, 60% of the 7400 students are female.The student newspaper reports results of a survey of a random sample of 50 students about various topics involving alcohol abuse, such as
The distribution of family size in a particular tribal society is skewed to the right, with μ = 5.2 and σ = 3.0.These values are unknown to an anthropologist, who samples families to estimate mean
Use the applet for the Sampling Distribution for the Sample Proportion at www.artofstat.com/webapps.html to illustrate this concept. Set the population proportion as 0.50 and sample size n = 100.(a)
Use the applet for the Sampling Distribution for the Sample Mean for continuous variables at www.artofstat.com/webapps.html to investigate the sampling distribution of ¯y.(a) Select the skewed
Go to the applet for the Sampling Distribution for the Sample Mean for discrete variables at www.artofstat.com/webapps.html.(a) Construct a population distribution that you think is plausible for y =
For a single toss of a coin, let y = 1 for a head and y = 0 for a tail, to simulate the vote in an election with two equally preferred candidates.(a) Construct the probability distribution for y, and
(Class Exercise) Refer to Exercises 1.11 and 1.12(pages 9 and 10). Using the population defined by your class or using the Students data file, the instructor will select a variable, such as weekly
Sunshine City was designed to attract retired people.Its current population of 50,000 residents has a mean age of 60 years and a standard deviation of 16 years. The distribution of ages is skewed to
(Class Exercise) Table 4.5 provides the ages of all 50 heads of households in a small Nova Scotian fishing village. The data are in the data file Ages at the text website. The distribution of these
(a) Which distribution does the sample data distribution tend to resemble more closely—the sampling distribution or the population distribution? Explain.(b) Explain carefully the difference between
The Palestinian Central Bureau of Statistics(www.pcbs.gov.ps) asked mothers of age 20–24 about the ideal number of children. For those living on the Gaza Strip, the probability distribution is
For a normal distribution, show that(a) The upper quartile equals μ + 0.67σ.(b) According to the 1.5(IQR) criterion, an outlier is an observation falling more than 2.7 standard deviations below or
In an exit poll of 2696 voters in the 2014 gubernatorial election in Florida, 50.5% said they voted for Rick Scott and 49.5% said they voted for Charlie Crist. Based on this information, would you be
For an election exit poll that uses random sampling, find the standard error of the sample proportion voting for a candidate for whom the population proportion is 0.50, when n = 100, when n = 1000,
The standard error of a statistic describes(a) The standard deviation of the sampling distribution of that statistic.(b) The standard deviation of the sample data.(c) How close that statistic is
The Central Limit Theorem implies that(a) All variables have bell-shaped sample data distributions if a random sample contains at least about 30 observations.(b) Population distributions are normal
True or False: As the sample size increases, the standard error of the sampling distribution of ¯y increases. Explain your answer.
4.54.* LakeWobegon Junior College admits students only if they score above 400 on a standardized achievement test. Applicants from group A have a mean of 500 and a standard deviation of 100 on this
4.55.* From the formula on page 72, the standard deviation of a discrete probability distribution is(a) When y can equal only 0 and 1, letting π = P(y = 1)and 1 − π = P(y = 0), show that μ = π
4.56.* Refer to the formula for the normal distribution curve shown in the footnote on page 72. Show that this curve is symmetric, by showing that for any constantc, the curve has the same value at y
4.57.* The standard error formula σ¯y = σ/√n treats the population size as infinitely large relative to the sample size n. The formula for σ¯y for a finite population size denoted by N isThe
4.58.* A general rule states that for independent observations, the variance of yi is the sum of the variances, which is nσ2 for n observations.(a) Explain intuitively why yi would have a larger
4.59.* Ellenberg (2014) noted that when you use sample data to rank states by brain cancer rates, the highest ranking state (South Dakota) and the nearly lowest ranking state (North Dakota) had

Showing 3600 - 3700 of 5757

First
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved