1 / 13

Probability – the bedrock of randomness

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. Approaches to probability.

joann
Télécharger la présentation

Probability – the bedrock of randomness

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 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

  2. 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?

  3. 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

  4. 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.

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

  6. 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

  7. Probability table

  8. Probability table

  9. Randomness and Probability • ‘Scientific sampling’ is random sampling • Simple • Stratified • Cluster • What? • Why? • How?

  10. What is random sampling? • Simple random sample -Every sample with the same number of observations has the same probability of being chosen • Stratified random sample – Choose simple random samples from the mutually exclusive strata of a population • Cluster sample – Choose a simple random sample of groups or clusters

  11. Why sample randomly? • To make valid statistical inferences to a population • Conclusions from a convenience sample can be questioned • Conclusions from a self-selected sample are SLOP

  12. How can samples be randomly chosen? • Random number generators (software) • Ping pong balls in a hopper • Other mechanical devices • Random number tables • Slips of paper in a ‘hat’

  13. Summary: Only inferences from random samples are valid 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 conditional probabilities.

More Related