16 chapter 6 nowsupposetherandomvariabletoworkwithis x

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online