# lec4 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

This preview shows pages 1–12. Sign up to view the full content.

MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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

View Full Document
Poisson Random Variable r(x) S.I. events p (1) in ∆ x r x r is constant x p ( n =0; L )= e rL 1 st element of p ( n ; L ) 8.044 L4B1
LL + L x 0 p ( n ; L +∆ L ) p ( n ; L ) p (0; ∆ L )+ p ( n 1; L ) p (1; ∆ L ) ± ²³ ´ ± ²³ ´ (1 r L ) ( r L ) dp ( n ; L ) p ( n ; L L ) p ( n ; L ) = rp ( n 1; L ) ( n ; L ) L dL 8.044 L4B2

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

View Full Document
± ²³ ´ ± ²³ ´ dp ( n ; γ ) Let γ rL + p ( n ; γ ) = p ( n 1; γ ) 1 st order, linear DE already known DE: γ is the variable and n is an index Probability: n is the variable and γ is a parameter 1 p ( n ; γ )= γ n e γ n ! 8.044 L4B3
Example Jointly Gaussian random variables t Random processes: Noise voltage or current v ( t ) ,i ( t ) Thermodynamic variable P ( t ) ,T ( t ) ( t ) Thermal radiation E ( t ) ,B ( t ) Seismic background signal s ( t ) 8.044 L4B4

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

View Full Document
t 1 t 2 =t 1 + τ v 1 v 2 t v(t) 2 ± 1 1 ρ 2 exp v 1 2 ρv 1 v 2 + v 2 p ( v 1 ,v 2 )= 2 2 πσ 2 2 σ 2 (1 ρ 2 ) σ is constant ρ = ρ ( τ ) 1as τ 0as τ →∞ 8.044 L4B5 0
v 1 v 1 v 1 v 2 v 2 v 2 ρ 1 ρ = 0 ρ -1 v 2 and v 2 are S.I. 8.044 L4B6

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

View Full Document

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

View Full Document

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.

## This note was uploaded on 11/08/2011 for the course PHYSICS 8.004 taught by Professor Staff during the Spring '08 term at MIT.

### Page1 / 12

lec4 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online