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

The Bayes’ theorem describes the probability of an event, based on conditions that Might be related to the event. Bayes’ theorem can also be calculated as the Joint probability divided by the marginal.
Bayes’ theorem deals with conditional probability.

????(????) ∗ ????(????|????) = ????(????) ∗ ????(????|????)

????(????|????)=P(A)P(B|A)/P(B)

????(????|????)=P(Ai)P(B|Ai)/ P(A1)P(B|A1)+ P(A2)P(B|A2)

????(????|????)=P(Ai ∩B) / P(A1∩B)+P(A2∩B)

-Discrete probab distrib(numb of students absent today, numb of books borrowed from library, number of head appering when a cons is tossed tre time)LIMITED

-Conitnous:liter of rain that occur in barcelona, the wheight of all population in spain )UNLIMITED.

Ejercicio Larry

Are indoeendent?

Not because

1. Many business owners spend years trying to get their enterprise started.

2. At the rate we are going, we are lucky to break even at year's end.

3. The world's biggest stock exchange is in New York.

4. Every employee has shares in the company.

5. The stock market rose 20% today. Brokers were euphoric!

6. The dip in the market caused some investors concern.

7. There was a dramatic rise in the share price at the end of the week.

8. Dividend is the part of the company's profits which is paid to shareholders.

9. One of the most difficult parts of running a restaurant is keeping the cashflow which can be variable.

10. House prices have increased by 5%. It is too expensive to buy now.

11. Demand for this product has fallen recently. We won't manufacture... Continue reading "Understanding Business and Stock Market Terminology" »

Queueing Models

M/M/s: Exponential arrival and service with more than one server. These models are needed in the economic analysis of the system.

M/G/1: Exponential arrival with general service time.

M/D/1: Exponential arrival with deterministic (fixed) service time. Because of lower variability in service time, performance measures are better than M/M/1.

Queues with priority: Performance measures will improve for high-priority customers and worsen for low-priority customers. However, performance measures averaged across all customers (high AND low priority) will remain the same as before.

Distinguish between the number of servers and the number of queues:

1. An M/M/2 queue with two servers but a single queue of waiting customers.
2. Two M/M/1 queues where

Cost Accounting and Budgeting Fundamentals

• FOH Allocation: Single Plantwide, Departmental, and Activity-Based Rates
• Advantages of Departmental FOH Rates: It doesn't assign other costs such as depreciation.
• Characteristics of Unit, Batch, Facility, and Product Level
• Activity-Based Costing and the Importance of Activity Drivers
• Importance of ABC Costing
• Importance of Matching Strategic Planning with Pricing, Market Penetration, and Expansion
• Contribution Margin Formula: Sales - Variable Costs (VC)
• Fixed Cost and Variable Cost Behavior
• Break-Even Point Concept and Formula: Level of sales at which contribution margin matches fixed expenses, expressed in dollars.
• Direct Labor (DL) Cost per Unit: Given two different levels of production
• Differences Between

The Production Volume Variance

Represents the difference between budgeted (incurred) and actual (allocated) fixed manufacturing costs.

When a greater proportion of costs are fixed costs, then

when demand is low the risk of loss is high

FALSE?

Gross Margin will always be greater than contribution margin.

Given a constant contribution margin per unit and constant fixed costs, the period-to-period change in operating income under variable costing is driven solely by:

changes in the quantity of units actually sold

In CVP analysis, the amount of units to be sold for the company to break even:

Increases when the contribution margin per unit decreases, all other things being equal

FALSE?

Nonmanufacturing costs are expensed in the future under variable costing.... Continue reading "Understanding Production Volume Variance and Costing Methods" »

Ch 12 Anova

Goal/purpose: Evaluate mean difference between 2 or more treatments

• Factor: The IV that designates the groups being compared
• Levels: Individual conditions or values that make up a factor
• Factorial design: A study that combines two or more factors

The Logic:

• Between treatment variance
  • Variability results from general differences between the treatment conditions
  • Variance between treatments measures differences among sample means
• Within treatments variance
  • Variability within each sample
  • Individual scores are not the same within each sample

Notations:
k= # of treatment condition
T= sum of squares for each treatment
G= grand total of all scores in study
N= total number of scores
kn= when all samples are same size
n1,n2= # of scores in each treatment

Post

3.11. QUESTIONNAIRE DESIGN

1.Roles of questionnaires: Primary purpose: facilitate the extraction of data from a respondent. Secondly: It serves as an ‘aide memoire’ to the interviewer.Thirdly: It provides consistency in the way the interview is conducted. Without a questionnaire: questions would be asked in a haphazard way at the discretion of the individual.

2.Types of questionnaires: Structured questionnairesconsist of closed or prompted questions (with predefined answers) that require the designer to anticipate all possible answers. Semi-structured questionnaires comprise a mixture of closed and open questions used in B2B market research where there is a need to accommodate a large range of different responses from companies.Unstructured... Continue reading "JOJO" »

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"" »