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Quantitative Methods Varsha Varde
Quantitative Methods Quantifying Uncertainty:  Basic Concepts of Probability
Quotes from You and Me ,[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Uncertainty ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Quotes from You and Me After This MBA ,[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Probability Theory ,[object Object],[object Object],Varsha Varde
Assigning Probabilities ,[object Object],[object Object],[object Object]
Assume equally likely outcomes
Use Relative Frequencies ,[object Object],[object Object],[object Object],[object Object],[object Object]
Subjective Probability ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Experiment ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Event ,[object Object],[object Object],[object Object]
EVENT/OUTCOME ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Sample space ,[object Object],[object Object]
Venn Diagram For Roll of a die A:Odd spots B:Even Spots
Equally Likely Events ,[object Object],[object Object],[object Object]
Exhaustive Events ,[object Object]
Independent Events ,[object Object],[object Object]
Dependent Events ,[object Object],[object Object]
Mutually Exclusive Events ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Notation . ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Venn Diagram A:Candidates over 3 years experience B:Candidates with post graduate qualification   S AB
More definitions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Probability of an event ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Basic Formula of Probability ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Rules of Probability:  Multiplication Rule   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Rules of Probability:  General Multiplication Rule   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Rules of Probability:  Addition Rule   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Rules of Probability:  General Addition Rule   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Exercise ,[object Object],[object Object],Varsha Varde
Solution ,[object Object],[object Object],[object Object],Varsha Varde
Conceptual Definition of Probability ,[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Steps in calculating probabilities of events ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Example. ,[object Object],[object Object],[object Object],[object Object],Varsha Varde
Probability Laws ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Law of total probability ,[object Object],[object Object],[object Object],[object Object],Varsha Varde
Bayes’ Law ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Bayesian Approach  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
P(Ai) P(B/Ai) P(AiB) P(AiB)/P(B)= P(Ai/B) Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities P(A1)=0.30 P(B/A1)=0.65  P(A1B)=0.195 P(A1/B)=.195/.37  =.527 P(A2)=0.70 P(B/A2)=0.25 P(A2B)=0.175 P(A2/B)=.175/.37=.473 P(B)=0.37
Example . ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
General Bayes’Theorom   ,[object Object],[object Object],[object Object],[object Object],[object Object]
Counting Sample Points ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Basic principle of counting: mn rule ,[object Object],Varsha Varde
Examples. ,[object Object],[object Object],[object Object],[object Object],Varsha Varde
Generalized basic principle of counting ,[object Object],Varsha Varde
Examples ,[object Object],[object Object],[object Object],[object Object],Varsha Varde
Examples ,[object Object],[object Object],[object Object],[object Object],Varsha Varde
Permutations:  (Ordered arrangements ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Combinations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Random Sampling ,[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Frequency Distribution: Number of Sales Orders Booked by 50 Sales Execs April 2006 Varsha Varde Number of Orders Number of SEs 00 – 04 14 05 - 09 19 10 – 14 07 15 – 19 04 20 – 24 02 25 – 29 01 30 – 34 02 35 – 39 00 40 – 44 01 TOTAL 50
Probability Distribution Varsha Varde Number of Orders Number of SEs Probability 00 – 04 14 0.28 05 - 09 19 0.38 10 – 14 07 0.14 15 – 19 04 0.08 20 – 24 02 0.04 25 – 29 01 0.02 30 – 34 02 0.04 35 – 39 00 0.00 40 – 44 01 0.02 TOTAL 50 1.00
Standard Discrete Prob Distns ,[object Object],[object Object],Varsha Varde
Standard Discrete Prob Distns ,[object Object],[object Object],Varsha Varde
Standard Continuous Prob Distn ,[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Features of Normal Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde
Probabilities in Normal Distn ,[object Object],[object Object],[object Object],[object Object],[object Object],Varsha Varde

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03+probability+distributions.ppt

  • 2. Quantitative Methods Quantifying Uncertainty: Basic Concepts of Probability
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15. Venn Diagram For Roll of a die A:Odd spots B:Even Spots
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21.
  • 22. Venn Diagram A:Candidates over 3 years experience B:Candidates with post graduate qualification S AB
  • 23.
  • 24.
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  • 26.
  • 27.
  • 28.
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  • 35.
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  • 37.
  • 38.
  • 39.
  • 40.
  • 41.
  • 42. P(Ai) P(B/Ai) P(AiB) P(AiB)/P(B)= P(Ai/B) Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities P(A1)=0.30 P(B/A1)=0.65 P(A1B)=0.195 P(A1/B)=.195/.37 =.527 P(A2)=0.70 P(B/A2)=0.25 P(A2B)=0.175 P(A2/B)=.175/.37=.473 P(B)=0.37
  • 43.
  • 44.
  • 45.
  • 46.
  • 47.
  • 48.
  • 49.
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  • 52.
  • 53.
  • 54. Frequency Distribution: Number of Sales Orders Booked by 50 Sales Execs April 2006 Varsha Varde Number of Orders Number of SEs 00 – 04 14 05 - 09 19 10 – 14 07 15 – 19 04 20 – 24 02 25 – 29 01 30 – 34 02 35 – 39 00 40 – 44 01 TOTAL 50
  • 55. Probability Distribution Varsha Varde Number of Orders Number of SEs Probability 00 – 04 14 0.28 05 - 09 19 0.38 10 – 14 07 0.14 15 – 19 04 0.08 20 – 24 02 0.04 25 – 29 01 0.02 30 – 34 02 0.04 35 – 39 00 0.00 40 – 44 01 0.02 TOTAL 50 1.00
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.