03+probability+distributions.ppt

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

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

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 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

03+probability+distributions.ppt

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