LectureSept8

# LectureSept8 - BME 423 Lecture Notes Sept 8 2008 Some Basic...

This preview shows pages 1–7. Sign up to view the full content.

Some Basic Probability Discrete Random Variables • Expected Value (Examples) Continuous Random Variables • Probability Density Function (pdf) • Cumulative Distribution Function (df) • Expected Value Using Standard Normal df Table BME 423 Lecture Notes - Sept. 8, 2008

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

View Full Document
Discrete Probability Mass (Density) Function f(x) = Prob(X=x) x f(x) 12345 k x xxxx x 12 () , , , 0 e l s e w h e r e ik f xx x x fx = Properties 0 i 1 1 k i i = =
Expected (or Mean) Value [] ( ) xD E Xx f x μ == x f(x) 1 2 1/2 Example () ( ) 11 12 1 . 5 22 EX x f x = =+ = Others Let X denote a discrete RV with values in set D and pdf f(x)

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

View Full Document
Expected Value of a Function of X Let X denote a discrete RV with values in set D and pdf f(x) ( ) ( ) ( ) [] xD E hX hx f x = Define a function of X as h(x) x f(x) 1 2 1/2 Example ( ) () [] () 2 2 2 2.5 1.5 0.25 X X EX X == =− =
How to describe the “degree of randomness” of a continuous RV X? () f x Prob( ) ( ) b a aXb f x d x <≤ = f ( x ) 100 200 0 x HR (beats/min) Prob(50 75) HR < Probability Density Function (Continuous RV) Properties () 0 fx 1 f xdx −∞ = Probability density function ( pdf ):

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

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

{[ snackBarMessage ]}

### Page1 / 21

LectureSept8 - BME 423 Lecture Notes Sept 8 2008 Some Basic...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online