Bayes' Theorem

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Questions and Answers

Haney's definition of business emphasizes which aspect?

  • Purely philanthropic endeavors
  • Charitable contributions
  • Social welfare activities
  • Wealth creation and processing (correct)

What is the minimum number of parties required for a business transaction to be valid?

  • An unlimited number, to ensure market competition
  • Three: a buyer, a seller, and a witness
  • One, representing a sole proprietorship
  • Two: a buyer and a seller (correct)

Which of the following best describes the 'profit motive' in business?

  • A focus on community service over financial gain
  • A desire to minimize sales volume
  • An attempt to reduce costs regardless of sales
  • The basic aim of increasing profits (correct)

Before goods and services are exchanged, what should business enterprises ensure?

<p>Goods are manufactured or procured for sale (A)</p> Signup and view all the answers

Which scenario exemplifies the 'exchange of goods and services' in a business context?

<p>Buying a notebook with money (D)</p> Signup and view all the answers

In the context of business, what distinguishes consumer goods from capital goods?

<p>Consumer goods directly satisfy human needs, while capital goods aid further production (A)</p> Signup and view all the answers

For a series of dealings to be considered a business activity, what element must be present?

<p>Regularity or continuity in transactions (B)</p> Signup and view all the answers

Which of the following activities is classified as a 'non-economic' activity?

<p>Cooking a meal for one's family (D)</p> Signup and view all the answers

What does 'distribution' encompass in the business context?

<p>Marketing and transfer of goods from producer to consumer (B)</p> Signup and view all the answers

How would categorizing converting oil seeds into edible oil with the help of man power and machine power impact a business?

<p>Considered an example of manufacturing of the goods (C)</p> Signup and view all the answers

Flashcards

Non-Economic Activities

Human activities performed to satisfy personal, social, religious, cultural, or sentimental requirements without monetary expectations.

Economic Activities

Activities involving production, distribution, and consumption of goods and services for money or money's worth.

Business

Organized efforts by individuals/groups to produce/sell goods/services for profit, satisfying societal needs.

Definition of Business (Haney)

Business activities are human activities directed towards the production and processing of wealth.

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Definition of Business (Pride, Hughes, Kapoor)

Organized efforts to produce and sell for a profit goods and services that satisfy society's needs.

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Business Activity

Business is an economic activity undertaken to earn money or livelihood.

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Two Parties

Every business transaction involves an exchange between a seller and a buyer.

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Profit Motive

The basic purpose is to earn profit by maximizing sales or reducing costs.

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Production of Goods and Services

Goods/services should be produced by business enterprises for sale to consumers.

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Exchange of Goods and Services

Business involves transfer of goods/services directly or indirectly for money/worth.

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Study Notes

Teorema de Bayes (Bayes' Theorem)

  • Describes the probability of an event based on prior knowledge of related conditions.

Formula

  • $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$
    • $P(A|B)$: Posterior probability of A given B.
    • $P(B|A)$: Probability of B given A.
    • $P(A)$: Prior probability of A.
    • $P(B)$: Prior probability of B.

Deduction of the Theorem

Diagrama de Venn (Venn Diagram)

  • Illustrates a sample space where events A and B can occur.
  • The overlapping area represents the probability of both A and B occurring.

Conditional Probability

  • The probability of an event occurring, given that another event has already occurred

  • $P(A|B) = \frac{P(A \cap B)}{P(B)}$

    • $P(A|B)$: Conditional probability of A given B.
  • Invert the roles of A and B

  • $P(B|A) = \frac{P(A \cap B)}{P(A)}$

    • $P(B|A)$: Conditional probability of B given A.

Solving for $P(A \cap B)$

  • $P(A|B)P(B) = P(A \cap B) = P(B|A)P(A)$

Teorema de Bayes (Bayes' Theorem)

  • $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$

Complex Numbers

Imaginary number

  • When squared, yields a negative result.
  • $ i = \sqrt{-1} $
  • $ i^2 = -1 $

Example

  • $\sqrt{-9} = \sqrt{9*-1} = \sqrt{9} * \sqrt{-1} = 3i $

Complex number

  • Expressed as a + bi, where a and b are real numbers, and i is the imaginary unit.
    • a is the real part.
    • bi is the imaginary part.

Example

  • 3 + 2i
    • 3 is the real part.
    • 2i is the imaginary part.

Operations

Addition

  • $(a + bi) + (c + di) = (a + c) + (b + d)i $

Example

  • (3 + 2i) + (5 - 4i) = 8 - 2i

Subtraction

  • $(a + bi) - (c + di) = (a - c) + (b - d)i $

Example

  • (3 + 2i) - (5 - 4i) = -2 + 6i

Multiplication

  • $ (a + bi)(c + di) = ac + adi + bci + bdi^2 $
    • $ = ac + adi + bci - bd $
    • $ = (ac - bd) + (ad + bc)i $

Example

  • $ (3 + 2i)(5 - 4i) = 15 - 12i + 10i - 8i^2 $
    • $ = 15 - 2i + 8 $
    • $ = 23 - 2i $

Division

  • $\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(ac + bd) + (bc - ad)i}{c^2 + d^2} $

Example

  • $ \frac{3 + 2i}{5 - 4i} = \frac{(3 + 2i)(5 + 4i)}{(5 - 4i)(5 + 4i)} $
    • $ = \frac{15 + 12i + 10i + 8i^2}{25 - 16i^2} $
    • $ = \frac{7 + 22i}{41} $
    • $ = \frac{7}{41} + \frac{22i}{41} $

Absolute Value

Also known as the Modulus

  • $ \left| a + bi \right| = \sqrt{a^2 + b^2} $

Example

  • $ \left| 3 + 4i \right| = \sqrt{3^2 + 4^2} $
    • $ = \sqrt{9 + 16} $
    • $ = \sqrt{25} $
    • $ = 5 $

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