Notes, summaries, assignments, exams, and exercises for Mathematics for Baccalaureate

Expected Returns and Risk Analysis

Suppose you won the lottery and had two options: (1) receiving $0.5 million or (2) taking a gamble in which, at the flip of a coin, you receive $1 million if a head comes up but receive zero if a tail comes up.

Lottery Decision Analysis

• a) What is the expected value of the gamble?
  ($1 million)(0.5) + ($0)(0.5) = $0.5 million
• b) Would you take the sure $0.5 million or the gamble?
  You would probably take the sure $0.5 million.
• c) If you chose the sure $0.5 million, would that indicate that you are a risk averter or a risk seeker?
  Risk averter.

Investment Scenarios: Bonds vs. Stocks

Suppose the payoff was actually $0.5 million and that was the only choice. You now face the choice of investing it in a U.S. Treasury bond...

Introduction to Statistics

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make informed decisions.

Types of Statistics

• Descriptive Statistics: Methods of organizing, visualizing, and summarizing information from samples or populations.
• Inferential Statistics: Methods of using information from a sample to draw conclusions regarding the population.

Example: A survey of 2,000 students (3rd to 12th grade) found that they devoted an average of 7 hours and 38 minutes each day to using electronic media.

Key Definitions

• Data: Information coming from observations, counts, measurements, or responses.
• Population: The collection of all outcomes, measurements, or responses (sometimes called a census). A numerical description

English Modal Verbs and Their Uses

Ability

• Can
• Could
• Be able to

Permission

• Can
• Could
• May

Requests, Suggestions, and Polite Orders

• Can
• Could
• Might

Possibility and Probability

• Could
• May
• Might

Obligation

• Must
• Have to

Necessity

• Need to

Mastering English Prefixes and Suffixes

Common Prefixes

• Disappear
• Unavoidable
• Mislead
• Illogical
• Immature
• Inaccessible
• Impolite
• Irrational
• Irregular
• Discontinue
• Insensitive
• Impersonal
• Non-smoker
• Illiterate
• Distrust
• Unconventional
• Unjustified
• Inconclusive

Prefix Rules:

• IM- is used before m or p.
• IL- is used before l.
• IR- is used before r.

Common Suffixes

• Photocopiable
• Countless
• Judgement
• Timeless
• Efficiency
• Exploration
• Rudeness
• Speechless
• Employment
• Dramatization
• Frequency
• Argument
• Awareness
• Recommendation
• Deceitful
• Careful
• Pointless
• Respectful
• Tendency
• Reliable

Fundamentals

Understanding Annuity Due

An annuity due is a series of equal payments made at the beginning of each period. Below are practical examples to help you master these calculations.

Example 1: Lease vs. Cash Purchase

You are buying a new vehicle and must decide between leasing or paying cash. The salesperson offers a cash price of $23,000 or a five-year lease with:

• Monthly payments of $300 (first payment due at signing).
• A buyout of $9,500 at the end of five years.

Since the first payment is made at the start, the lease requires 59 additional equal payments. Assuming a 6% annual interest rate compounded monthly (0.5% per month):

• BGN Mode: N = 60, I = 0.5, FV = $9,500, PMT = $300
• Result: CPT PV = –$22,638

Conclusion: The lease is the better deal because...

Merchandise Accounting

CGPUR (Cost of Goods Purchased): (Discounts + Returns + Allowances) = CGPUR. CGS (Cost of Goods Sold): Beginning Merchandise Inventory + CGPUR = Cost of Goods Available for Sale - Ending Merchandise Inventory = CGS. Income Statement: Revenue - CGS = Gross Margin - Operating Costs = Operating Income.

Manufacturing Cost Accounting

CGMAN (Cost of Goods Manufactured):

• Direct Materials: Beginning Direct Materials Inventory + Purchases of Direct Materials = Cost of Direct Materials Available for Use - Ending Inventory = Direct Materials Used.
• Indirect Manufacturing Costs: Indirect Manufacturing Labor + Plant Insurance + Depreciation + Repairs & Maintenance = Total Indirect Manufacturing Costs.
• Total Manufacturing Costs: (Direct

Visualizing Discrete and Continuous Data

We can use bar charts to describe data from a discrete variable. In this case, we can perform additional analysis: first, create a frequency table, then draw the charts.

Cumulative Bar Charts

In addition to the standard bar chart, we can draw a cumulative bar chart:

• The standard bar chart allows for comparison among groups.
• The cumulative bar chart displays percentages.
• Note: Cumulative bar charts require an inherent order among outcomes, so they are not suitable for categorical variables.

Histograms for Continuous Variables

Histograms are the equivalent of bar charts for continuous variables:

• To draw a histogram, you must first group the data, similar to building a frequency table.
• Key Difference: In a histogram,

Chapter6: Absorption: DM+DL+Varaible MOH+Fixed MOH.....Variable: DM+DL+VariableMOH...

Parametric Inference Fundamentals

The probability distribution of the population under study is known, except for a finite number of parameters. Its goal is to estimate those parameters. Examples include the T-test and ANOVA.

Non-Parametric Inference Basics

The distribution of the population is not known. It is used to test the assumptions of parametric methods, for example, to check if the population distribution is normal.

What is a Statistic?

A random variable function of the sample that does not depend on the unknown parameter.

Understanding Estimators

A statistic whose values are acceptable for estimating an unknown parameter.

Unbiasedness in Estimation

We do not allow systematic overestimation or underestimation of the parameter, which would result...

Annual Accounts

• Balance Sheet: Reflects the equity, representing the resources available to the employer to carry out activities.
  • Profit and Loss Account: Measures the income generated by the business.
  • Statement of Changes in Equity: Collects the variation in the company's equity.
  • Cash Flow Statement: Reports on the origin and use of monetary assets, representing cash and cash equivalents classified by activity.
  • Notes to the Accounts: Expands the information collected in the annual accounts and contains additional details.

Corporate Social Responsibility and Audits

• Social Balance of the Company: A document that extends the study of the business's effects on its environment, determining direct or indirect impacts on public welfare.
• Audit: An analysis