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

Decision Alternatives and States of Nature

Alternatives are options for a decision. Outcomes are influenced by random factors beyond control, known as states of nature. Prior probabilities indicate the likelihood of each state. Each alternative and state combination yields a payoff, often monetary.

Decision-Making Approaches

1. Optimistic Approach

Maximax (Profit)

Choose the alternative with the highest possible payoff.

Minimin (Cost)

Choose the alternative with the lowest possible cost.

2. Conservative Approach

Maximin (Profit)

Choose the alternative with the best worst-case payoff.

Minimax (Cost)

Choose the alternative with the lowest worst-case cost.

3. Minimax Regret

Minimize the maximum regret by constructing a regret table.

4. Expected Value (Bayes'

Finance Essentials

Key Concepts

Time Value of Money

• Future Value: Amount to which an investment will grow after earning interest
• Present Value: Value today of a future cash flow

Interest

• Compound Interest: Interest earned on interest
• Simple Interest: Interest earned only on the original investment
• Annual Percentage Rate (APR): Interest rate that is annualized using simple interest
• Effective Annual Rate (EAR): Interest rate that is annualized using compound interest

Cash Flow Streams

• Annuity: Equally spaced level stream of cash flows for a limited period of time
  • Ordinary Annuity: End of period cash flows
  • Annuity Due: Beginning of period cash flows
• Perpetuity: A stream of level cash payments that never ends

Bonds

• Bond: Security that obligates the issuer to make

9.14 Nonconstant growth. Computech corporation is expanding Rapidly and currently needs to retain all of its earnings; hence, it does not Pay dividends. However, investors expect computech to begin paying dividends, Beginning with a dividend of $0.50 coming 3 years from today. The dividend Should growth rapidly at a rate of 35% per year during years 4 and 5; but after Year 5, growth should be constant 7% per year. If the required return on computech Is 13%, what is the value of the stock today?

solution

Calculate the dividend cash flows and place them on a time Line.  Also, calculate the stock price at The end of the supernormal growth period, and include it, along with the Dividend to be paid at t = 5, as CF5.  Then, enter the cash flows as... Continue reading ""interest of delay"" »

Chapter 1

- Information systems today are ubiquitous

1) If a toy company is planning to introduce 3 new toys next Christmas. The toys sales can be a success or a failure, what is the probability that at least 2 of the toys are a success?

FFF FFS FSF FSS 4/8 = ½ = 0.5

S SFF SFS SSF SSS

For problems 2 and 3: a guitar manufacturer has an average daily production of 60 units, with a standard deviation of 7 units per day. If the guitar production distribution is mound shape:

2) What percentage of days in a month will have a daily production between 53 and 74 units?

53

3) What percentage of days in a month will have a daily production of more than 67 units?

x>67 = 16%

4) A combination lock system has three ten-digit (0 to 9) number wheels side by side. How many four-digit opening numbers are possible if... Continue reading "Probability and Statistics Problems with Solutions" »

unit 14.WORKING WITH THE TEXT

1.‐ Niamh is the student participating in the Erasmus pro

2.‐ a.‐ “we should all apply for it.” Recommendation that

all students apply for the Erasmus project b.‐ “we all

were still grateful” they were grateful despite not getting

what they wanted. C.‐ “After filling out papers and

forms” Completing the paperwork for the project

d.‐ “I would like to set up” she wants to begin the

creation of something. E.‐ “regardless of studying

Spanish for a year.” Despite studying Spanish during one

year she knew none. 3.‐ a.‐ It was good to know

someone spoke English. B.‐ They took him to the local

farm. C.‐ Because she gained experience and that would

be useful in the future.

VOCABULARY a.‐ English... Continue reading "Concept of education" »

Escenario 1: Proyección Inicial

Write your tLecture 1

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" »