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BUSA 3321 - Probability

BUSA 3321 - Probability. Probability – the bedrock of randomness. Definitions Random experiment – observing the close of the NYSE and the Nasdaq Sample space = {NYSE+Nasdaq+, NYSE+Nasdaq-, NYSE-Nasdaq+, NYSE-Nasdaq-} Simple event = {NYSE+Nasdaq+} Event = the NYSE is up.

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BUSA 3321 - Probability

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  1. BUSA 3321 - Probability

  2. Probability – the bedrock of randomness • Definitions • Random experiment – observing the close of the NYSE and the Nasdaq • Sample space = {NYSE+Nasdaq+, NYSE+Nasdaq-, NYSE-Nasdaq+, NYSE-Nasdaq-} • Simple event = {NYSE+Nasdaq+} • Event = the NYSE is up

  3. Approaches to probability • Classic – equal likelihood • Dice, cards, inventory control, polls, audits – (random samples) • Relative frequency – historic data, relative frequency distributions • Actuarial tables • Race track odds • Subjective • Which for the NYSE and the Nasdaq?

  4. Probabilities of Combinations of Events • Union of sets – “or” • The NYSE is up or Nasdaq is up • Intersection of sets – “and” • Joint events • The NYSE is up and theNasdaq is up

  5. Conditional Probability P (A|B) = P(A and B)/P(B) A and B are independentif P(A|B) = P(A) Which also means that P(B|A) = P(B) Probability the Nasdaq is up given that the NYSE is up.

  6. Rules of Probability • Complement • Addition • General • Special • Multiplication • General • Special

  7. Rules: Complement: P(A complement) = 1 – P(A) Addition: P(A or B) = P(A) + P(B) – P(A and B) P(A or B) = P(A) + P(B) if A and B are mutually exclusive Multiplication:P(A and B) = P(A|B) * P(B) P(B|A) * P(A) P(A and B) = P(A) * P(B) if A and B are independent

  8. Probability table

  9. Probability table

  10. Diagnostics and False Positives

  11. Summary: The approach to assigning probabilities must be chosen: any probability must be between 0 and 1, inclusive the probability of the sample space is 1 The language of probability is the language of set theory. Learn the complement, addition and multiplication rules. Tables help in determining joint and marginal probabilities.

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