Lecture11_print

# Lecture11_print - MA/STAT416 Probability Lecture Notes...

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

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

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

Unformatted text preview: MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 7: Continuous Random Variables April 1, 2011 7 Density Functions, CDF, Quantile Function 7.1 The Probability Density Function (pdf) and Cumulative Distribu- tion Function (CDF) Definition. Let X be a real-valued random variable taking values in R . A function f ( x ) is called a probability density function if and only if f ( x ) ≥ ∀ x ∈ R , and Z ∞-∞ f ( x ) dx = 1 . Note: P ( a ≤ X ≤ b ) = Z b a f ( x ) dx. Definition. Let X be a real-valued random variable with a pdf f ( x ). Then, the cumulative distribution function of X is defined by F ( x ) = P ( X ≤ x ) = P ( X < x ) = Z x-∞ f ( t ) dt. Remark. f ( x ) = F ( x ). Definition. Let F ( x ) be the CDF of X . The median of X is the number m such that F ( m ) = 0 . 5 . Definition. Let X have the CDF F ( x ). Let 0 < p < 1. The p th quantile of X is defined to be the first x such that F ( x ) ≥ p .: F- 1 ( p ) = infx : F ( x ) ≥ p....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Lecture11_print - MA/STAT416 Probability Lecture Notes...

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

View Full Document
Ask a homework question - tutors are online