Notes, summaries, assignments, exams, and problems for Mathematics

Which of the following is most likely an issuer bonds: HEDGE FUND

A bond issued by a city would most likely be classified as a: NON-SOVEREIGN GOVERNMENT BOND

A fixed-income security issued with a maturity at issuance of nine months is most likely classified: MMSECURITY

The price of a bond issued in the US by a British company and denominated in US dollars is most likely: CHANGE AS US INTEREST RATES CHANGE

Interbank offered rates are best described as the rates at which major banks can: BORROW UNSECURED FUNDS

A company issues floating-rates bonds. The coupon rates is expressed as the three-month Libor plus a spread. The coupon payments are most likely: LIBOR INCREASES

A 10-year bond was issued four years ago. The bond is denominated in US dollars,

Taylor Series

f(x+h) = f(x) + f'(x)h + f''(x)h² /2! + f'''(x)h³ /3! + ...

Secant Method (Find Root)

1. Rewrite as f(x)=0
2. Set initial points
3. f'(x₂) = (f(x₂) - f(x₁)) / (x₂-x₁)
4. New point becomes x₂
5. Iterate

LU Decomposition

A = LU

Crout's

Identity top

Doolittle

Identity bottom

1. Set up LU
2. Find components through matrix multiplication and solve for variables

Solving for b matrix

LUX=B

1. Set UX = Y
2. Solve LY = B using algebra
3. Solve UX = Y using algebra

Norm

Absolute value of the largest row sum

Condition

||A||_inf||A^-1||_inf

Gauss-Seidel

1. Set each equation to a variable
2. Use any initial values for the first equation
3. Use the x₁ from the first equation to solve x₂
4. Iterate (Fast version of Jacobi Method)

Discrete Least Squares Approximation

AX = B

1. Make matrix A by [ n ∑(x) ∑(x²) ...]
2. Make

Portfolio Theory and Expected Returns

1. Expected return of the portfolio: μ_P = w₁μ₁ + w₂μ₂.

Standard deviation of the portfolio return: σ_p = √(w₁²σ₁² + w₂²σ₂² + 2ρw₁w₂σ₁σ₂).

• Suppose two investments R₁ and R₂ with expected returns μ₁ and μ₂.
• w₁ is the proportion of money in the first investment.
• σ₁ and σ₂ are the respective standard deviations.
• ρ is the coefficient of correlation between the two investments.

Market Portfolio and Systematic Risk

2. Relationship between any investment and the market portfolio: R = a + βR_M + ε.

• R = return from investment.
• R_M = return from market portfolio.
• a and β are constants.
• ε is a random variable representing the regression error.
• βR_M: Systematic risk.
• ε: Non-systematic risk.

Capital Asset Pricing

What are Standard Data Systems (SDS)?

A Standard Data System (SDS) is a database of normal time values organized by work elements. It is used to establish time standards for tasks composed of those work elements. A key feature is that time standards can be established before the job is actually performed.

When is an SDS Suitable?

A Standard Data System is particularly suitable in situations involving:

• A high degree of similarity between tasks.
• Batch production environments.
• A large number of standards that need to be set.
• The need to set standards before production begins.

Using a Standard Data System

The process for using an SDS typically involves the following steps:

1. Analyze the new tasks and divide them into their constituent work elements.
2. Access

E-Business and Its Impact

The Changing Landscape of Business

The rise of the internet has dramatically transformed the business landscape, giving rise to the concept of e-business. E-business encompasses a wide range of activities, including B2B (business-to-business) and B2C (business-to-consumer) transactions, supply chain management, and customer relationship management.

Key Characteristics of E-Business

• Integration: E-business systems integrate various business functions and channels, such as brick-and-mortar stores, online platforms, and mobile apps.
• Flexibility: E-business frameworks are designed to be flexible, open, and adaptable to changing market conditions.
• Ubiquity: E-business infrastructure enables ubiquitous commerce, allowing businesses

Single-Factor ANOVA is used to determine whether three or more populations have equal means.

ANOVA Assumptions:

• The population values are normally distributed.
• The variances for each population are equal.
• The samples are independent.
• The data measurement is interval or ratio level.

ANOVA is an analysis of variance. It needs to have equal variance in order to test the means.

Single-Factor ANOVA: analysis of variance design in which independent samples are obtained from two or more levels of a single factor for the purpose of testing whether the levels have equal means.

Type of data used in ANOVA: ratio or interval data (numbers).

H₀: all means are equal.

H₁: there is a difference in means.

Theory: Practicality.

In Multifactor ANOVA:

• Groups: rows (router

IFRS for SMEs: Accounting Policies, Estimates, and Errors

Understanding Accounting Policies, Estimates, and Prior Period Errors

Statement Evaluation:

• Statement: "While accounting for particular transactions, events, or conditions, entities are allowed to deviate from basic requirements imposed by IFRS for SMEs, but only if the effect of following the existing IFRS for SMEs guidance will not be material."
• Truthfulness: This statement is False. IFRS for SMEs generally requires adherence to its principles. Deviation is not permitted simply based on materiality; materiality primarily affects disclosure, not the application of recognition or measurement principles.

What Changes are Treated as Changes in Accounting Policy?

A change is treated as a change... Continue reading "IFRS for SMEs: Accounting Policies, Estimates, and PPE Principles" »

Fixed Costs

Fixed costs are not a function of the output. They do not vary with the output. They cannot be avoided until the operation of the firm is closed. They are contractual (prime).

Recurring and Non-Recurring Costs

• Recurring: Predetermined expenses for running the business, e.g., salaries, repairs, maintenance.
• Non-Recurring: Not predetermined, regular budgeting, e.g., repair of a machine. Sometimes it is also planned.

Cost Estimation

Cost estimation is the process of finding an estimate, an approximation of a value, which will be used for some purpose, though it is completely uncertain and unstable. Estimation is typically a value from statistics used to estimate the value of a corresponding population parameter.

Learning Curve

The learning... Continue reading "Cost Estimation and Management Decision Areas in Business" »

Qualitative and Quantitative Variables

Qualitative: variables that are not numerical. They represent categories or groups that the data can fall into. Nominal: the categories do not have a natural order or ranking. The key characteristic of nominal variables is that the different categories are mutually exclusive and there is no inherent order to the categories. Ordinal: the categories have a logical or natural order. However, the distances between the categories are not necessarily meaningful.

Quantitative: variables that represent quantities and can be measured numerically. Discrete: a type of quantitative variable that can take on a countable number of distinct values. These are typically values that you can list or count. They often represent... Continue reading "Understanding Data Types and Sampling Methods" »

Practicing material for Quiz #5 – Discrete Probability Distribution SOLUTIONS

1. The manager of a baseball team has determined that the number of walks, x, issued in a game by one of the pitchers is described by the probability distribution given below.

1. This pitcher issues as few as 0 walks and as many as 5 walks in a game.

1. Determine the following probabilities

i. P(x = 2) = 0.15

ii. P(x > 4) = 1 – 0.10 = 0.90

iii. P(x > 5) = 0

iv. P(2 < x < 4) = 0.15+0.45+0.15 = 0.75

1. Calculate the mean for this discrete probability distribution, µ = 2.85 walks

µ = Sxp(x) = 0(0.05) + 1(0.10) + 2(0.15) + 3(0.45) + 4(0.15) + 5(0.10) = 2.85

1. The average, over time, of walks issued in a game by one of the pitchers is 2.