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

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Descriptive statistics: Describe and summarize the data from the sample.

Probability models describe a model For the population which can be used to make probability statements about what Can be seen in the sample.

Statistical Inference goes in the Other direction. It uses the data in the sample to make inference about Features of  the population with Associated confidence and/or error bounds.

SPSS: Rows are subjects/units which are also Referred to as cases.

Columns are Things which are being measured on the cases. These are called variables.

Examples:

Obtaining Frequency tables:

Analyze -> Descriptive Stats -> Frequencies

Bar Graph: Graphs -> Legacy Dialog -> Bars -> Simple -> Category Axis (zyg)

Pie Chart:... Continue reading "Blood test "solt" »

Statistics: The Science of Organizing Data

Statistics is the science of organizing data to draw conclusions or answer questions.

Descriptive Statistics

Descriptive statistics describe data through numerical summaries and graphs.

Variables

Variables are characteristics of individuals within the population.

Discrete and Continuous Variables

Discrete variables are counted, while continuous variables are measured.

Nominal and Ordinal Variables

Nominal variables are named, while ordinal variables are ranked or ordered.

Interval and Ratio Variables

Interval variables have no meaningful zero and equal intervals between values, while ratio variables have a meaningful zero.

Types of Variables in a Study

The response variable is what is being studied, the explanatory... Continue reading "Introduction to Statistics" »

Vocabulary Builder: 35 Essential Words

A

1. Agonized

Manifesting, suffering, or characterized by great physical or mental pain.

2. Ample

Large and accommodating.

3. Assent

The expression of approval or agreement.

B

4. Befall

(Of something bad) happen to someone.

C

5. Chariots

A two-wheeled horse-drawn vehicle used in ancient warfare and racing.

6. Conceive

Become pregnant with (a child). Form or devise (a plan or idea) in the mind.

7. Cordial

Friendly, warm.

D

8. Dews

Moisture condensed from the atmosphere, especially at night, and deposited in the form of small drops upon any cool surface.

9. Divine

Of, from, or like God or a god.

10. Doe

Female deer.

F

11. Foe

An enemy or opponent.

G

12. Gossamer

Used to refer to something very light, thin, and insubstantial or delicate.... Continue reading "Vocabulary Builder: 35 Essential Words with Definitions" »

Financial Market Scenarios: Fixed Income and Derivatives

Sildavia: Term Structure and Yield Curve Construction

In Sildavia's financial market, we assume the existence of a series of zero-coupon bonds and conventional bonds. Each bond type presents specific traits:

• Zero-Coupon Bonds: Defined by spot rates and coupon interest rates.
• Conventional Bonds: Defined by specific characteristics (data assumed to be provided in an accompanying table).

Based on the provided data, the objective is to construct the TSIR (Term Structure of Interest Rates) and the Yield Curve for both kinds of bonds.

Moravia: Calculating Forward Rates

Considering the TSIR shown in Table 1, calculate the corresponding forward rates (r_t).

Furthermore, if the market involves an inverted

This document outlines the steps to calculate production costs, including equivalent units and costs for work-in-progress (WIP) and finished goods.

1. What does boot mean?
2. How to determine the basis of taxable and non-taxable stock dividends?
3. How to determine if a gain is long-term or short-term?
4. How does capital gain/loss netting work?
5. What is the tax rate of regular long-term capital gain? [0%, 15%, 20%]
6. Individual taxpayers can deduct net capital loss (short-term or long-term) up to $3,000 per year.
7. The maximum tax rate for collectibles is 28%; the maximum tax rate for unrecaptured Section 1250 gain is 25%.
8. How to determine amount realized? How to determine amount realized when there is debt assumption?
9. What is unrecaptured Section 1250 gain? How to calculate it?
10. What is the basis of gifts? How to determine the holding period of a gift?
11. How to determine the adjusted basis?
12. How to determine realized

Monthly Financial Data

1. Present Value of an Investment

15 Years Case

Present Value of the Investment = $4,900 [ (1/0.08) − (1/0.08(1 + 0.08)^15)] = $41,941.45

2. Effective Annual Rate (EAR)

EAR = (1 + (APR/m))^m − 1 If m becomes infinite, EAR = e^APR − 1

7% APR and quarterly compounding: EAR = (1 + (0.07/4))^4 − 1 = 7.19%

16% APR and monthly compounding: EAR = (1 + (0.16/12))^12 − 1 = 17.23%

11% APR and daily compounding: EAR = (1 + (0.11/365))^365 − 1 = 11.63%

3. Value of a Perpetual Stream of Payments

Present Value of the Perpetuity = (Payment/Interest Rate) Payment = $2,500, Interest Rate = 0.061

PV of the perpetuity at date t=14 is $2,500/0.061 = $40,983.61. Discounting it back to date t=7, we should have PV7 = $40,983.61/(1+0.061)^7 = $27,077.12.

4. Bond