normnotes

normnotes - Normal and Lognormal Distributions...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Normal and Lognormal Distributions – De…nitions/Notes De…nition 1 A continuous random variable X is said to have a normal distribution with para- meters ¹ and ¾ (or ¹ and ¾ 2 ), where ¡1 < ¹ < 1 and 0 < ¾ , if the pdf of X is: f ( x ; ¹;¾ ) = 1 ¾ p 2 ¼ exp à ¡ ( x ¡ ¹ ) 2 2 ¾ 2 ! , for ¡1 < x < 1 . De…nition 2 The normal distribution with parameter values ¹ = 0 and ¾ = 1 is called a standard normal distribution . A random variable that has a standard normal distribution is called a standard normal random variable and will be denoted by Z . The pdf of Z is: f ( x ;0 ; 1) = 1 p 2 ¼ exp à ¡ z 2 2 ! , for ¡1 < z < 1 . The cdf of Z is P ( Z · z ) = R z ¡1 f ( y ;0 ; 1) dy , which we will denote by ©( z ) . Notation z ® will denote the value on the measurement axis for which ® of the area under the z curve lies to the right of z ® . Proposition 1 If X has a normal distribution with mean ¹ and standard deviation ¾ , then Z = X ¡ ¹ ¾ is a standard normal random variable.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/08/2012 for the course EXST 4050 taught by Professor Staff during the Fall '10 term at LSU.

Page1 / 2

normnotes - Normal and Lognormal Distributions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online