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

Key Statistical Concepts

Variables

Categorical (Qualitative) Variables: Represent characteristics or qualities. Examples include race and gender.

Quantitative Variables: Represent numerical values that differ in magnitude.

Scales of Measurement

• Nominal: Unordered categories.
• Ordinal: Ordered categories.
• Interval: Equal intervals between values.

Data Visualization

Frequency: Displays the possible values of a variable and the number of times each occurs.

Histogram: A bar graph of frequencies or percentages. Shapes can be bell-shaped, skewed, or bimodal.

Box Plot: Displays the distribution of data, including median, quartiles, and outliers.

Scatter Plot: Shows the relationship between two variables.

Distribution

• For symmetric distributions, the mean equals

Revenue and Cost Formulas

• Revenue = Selling price per unit × Number of units sold
• Variable costs = Variable cost per unit × Number of units sold
• Total costs = Fixed costs + Variable costs
• Profit = Total revenue − Total costs or Total contribution − Fixed costs

Market and Investment Metrics

• Market capitalisation = Number of issued shares × Current share price
• Expected value (A & B) = (Pay-off of A × Probability of A) + (Pay-off of B × Probability of B)
• Net gain = Expected value − Initial cost of decision
• Market growth (%) = (Change in market size / Original market size) × 100
• Market share (%) = (Sales of one product or business / Total sales in the market) × 100
• Added value = Sales revenue − Cost of bought-in goods and services

Operational

CLARE FGF

1.- It was a long time since she had B carried

2.- Asked Bruno to address her C close

3.- A strong feeling of excitement D the average

4.- Having something to eat and B month compared

5.- Having something in common C growth, although

6.- She thought he might react B figure obtained

7.- Interested only in how she A researches put

8.- She discovers a way of D greater awareness

9.- Is in C line

RA:TS

10.- Nails A tend

9.- Record. D that

10.- Exception. H parti

11.- Sigh. F with

12.- Moment. A two

13.- To. C nowd HTTDFB

14.- Hugely. G it

15.- Strange. E when

14.- Country, Something

15.- Of such

WP

16.- Regularly B

17.- No longer C

18.- Tries to D

19.- Accepts C

20.- Is disa A

21.- Prefers D

22.- Is not A

23.- Now B

24.- Now D

25.- Likes to tell D

26.- Goes C -------

1) What is an Inverse Matrix and How Do You Calculate It?

A matrix A^-1 is called the inverse matrix of a matrix A (nxn) if AxA^-1= A^-1xA=E (where E is the identity unit matrix).

We calculate it by performing row operations on the augmented matrix (A | I) to transform it into (I | B). If this reduction is possible, then B=A^-1, which is the inverse matrix of A.

2) Define the Model of a Game

Games can be modeled in various forms:

• Tree Form Model (Game Tree): Represents the game as a sequence of decisions (moves) made by players.
• Normal Form Model: Represents the game using:
  • List of players
  • List of strategy spaces for each player
  • List of payoff functions (decision matrix) defining outcomes for each combination of strategies.
• Characteristic Function Form:

Health Insurance Reimbursements

• If the amount reimbursed by the employer equals the expenses incurred, the reimbursement is tax-neutral.

Amortizing R&D Benefits

• Costs are not amortized until benefits are received.
• Amortization Formula: Amortization Expense = Total R&D Expenditures × (Months of Benefits / 60).
• Example: $165,000 total R&D × (4/60).
• If the project is unsuccessful, total expenditures are tax-deductible as losses up to $250,000.

Life Insurance and Death Benefits

• Accrued Salary: Salary earned before death remains taxable.
• Employer Death Payments: Payments made to support a family are considered charitable and are not taxable.
• Insurance Benefits: Life insurance proceeds are excluded from gross income, though interest earned on

KEYS

1. You must be wondering why I haven’t phoned you.

2. The heavy rain prevented us from having the picnic we had planned.

3. Recently, there has been a rise in the number of people who study a degree.

4. It was a matter of minutes before the police came.

5. Can anyone come up with a solution to this problem?

6. Are you accusing me of not telling the truth about what happened?

7. I haven’t got round to phoning you, but I’ll do it soon.

8. Economists say that there is no doubt that the situation will get better.

9. It was my mother who/that got me interested in reading.

10. What is that’s causing you such a lot of confusion?

11. She made a very quick decision without giving enough thought to the matter.

12. It was a while until/ till/ before... Continue reading "Common English Phrases and Expressions for Language Learners" »

Introduce Research

• Study design/methods
• Appraisal
• Interpretation
• Application/utilization

Understand

• Evidence Informed Decision Making Model
• Sources of Evidence
• Types of research that inform practice (quantitative, qualitative, mixed methods)
• Why research studies should be critically appraised

1.2 Research, EBP & EIDM

• There are different ways of knowing; Empirical, Personal, Aesthetics, Ethical

1. Empirical (focus of class)

• Theories, models, facts
• Validation, confirmation
• Scientific competence

2. Personal knowledge

• Person stories, self
• Reflection, response
• Therapeutic use of self

3. Aesthetics knowledge

• Experience of nursing, health, illness
• Appreciation, grasp meaning
• Transformative act/acts

4. Ethical Knowledge

• Principles, codes
• Justification, dialogue

Evidence-Based Practice... Continue reading "HTHSCI 3CO4 Cheat Sheet" »

Chapter 6 Review: Bond Valuation Problems

1. Coupon Rate Calculation

   A $1,000 face value bond is currently quoted at 100.8. The bond pays semiannual payments of $22.50 each and matures in six years. What is the coupon rate?

   Coupon rate = ($22.50 × 2) / $1,000 = 0.0450, or 4.50 percent

2. Current Price of a Bond

   A $1,000 face value bond currently has a yield to maturity of 8.22 percent. The bond matures in five years and pays interest semiannually. The coupon rate is 7.5 percent. What is the current price of this bond?

   FV = 1000; PMT = 75/2 = 37.5; N = 5 x 2 = 10; I/Y = 8.22 / 2 = 4.11 => PV = 970.96

3. Determining Coupon Rate

   A six-year, semiannual coupon bond is selling for $991.38. The bond has a face value of $1,000 and a yield to maturity of 9.19