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QT1 - 06 - Normal Distribution

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Prithwis Mukerjee
Prithwis Mukerjee

Class notes used in Quantitative Techniques - I course at Praxis Business School, Calcutta

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Normal Distributions Q U A N T T E C H I N T E U Q I A S E V I T 1 0 S
Continuous Random Variable ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Probability of a Continuous Variable ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Distribution Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],The sum of the probabilities of ALL possible values of the random variable MUST be equal to 1
Density Function ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
What do these graphs mean ? ,[object Object],[object Object],[object Object],[object Object],[object Object]
Characteristics of a Normal Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Three very similar terms ! ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
From Density to Distribution ,[object Object],[object Object],[object Object]
Area under the Density curve ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Area under the Density curve ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],m =1.5 s 2 s A B C 2.25% 16%
The 2 s limit ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],m =1.5 2 s A C1 2.25% C2 2 s 2.25%
Problem Type A ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Solution to Shirt Problem P( x <= 20) = 0.11 P (x > 35) = 1 – 0.73 = 0.27 P (27 < x <= 32) = 0.6 – 0.35 = 0.25
Problem Type B ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Solution to Shirt Problem
Mostly 2 Categories of Problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Plus the issue of “range” ,[object Object],[object Object],[object Object]
Before the Era of Spreadsheets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Standard Normal Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Identical Distribution Functions

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QT1 - 06 - Normal Distribution