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Unformatted text preview: mulative distribution function for the standard normal random variable: Z= X − μX
~ N(0 , 1) σX The textbook tables are: (1) Appendix Table 1, pages 841‐2. (2) Inside front cover Appendix Table 1 will be used in the work here. 14 Chapter 6 How is the table read ? A graph is useful. Probability Density Function (PDF) of Z Area = 1 - F(z0) f(z) Area = P(Z < z0) = F(z0) 0 z0 z For a value of interest z0 the table gives the cumulative probability: F(z0 ) = P(Z ≤ z0 ) The table lists values for z0 ≥ 0 only. From symmetry of the normal distribution: F(− z0 ) = P(Z ≤ − z0 ) = P(Z ≥ z0 )
= 1 − F(z0 ) 15 Chapter 6 A result for a range probability with symmetric upper and lower values can be stated. For some value z0 : P(− z0 ≤ Z ≤ z0 ) = P(Z ≤ z0 ) − P(Z ≤ − z0 ) = F(z0 ) − [1 − F(z0 )]
= 2 F(z0 ) − 1 This is shown with a graph. PDF of Z f(z) Area = F(z0) - F(-z0) Lower Tail Area = F(-z0) -z0 Upper Tail Area = 1 - F(z0) 0
z z0 By symmetry of the normal distribution the area in the “lower tail” is identical to the area in the “upper tail.” 16 Chapter 6 Now suppose the random variable to work with is: X ~ N(μ , σ 2 ) For two numerical values a and b, with a < b, a probability of interest is: P(a < X < b) This probability statement can be transformed to a probability statement about the standard normal random...
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This note was uploaded on 02/06/2014 for the course ECON ECON 325 taught by Professor Whistler during the Spring '10 term at The University of British Columbia.
- Spring '10