This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: UCF Physics: AST 5765/4762: (Advanced) Astronomical Data Analysis Fall 2008 Lecture Notes: 8. Probability Distributions and Error Analysis 1 Check in: 2:00 — 2:10, 10 min • Did anyone notice errors in Bevington equations? 1 HW problem extra credit for first time each reported. • Bevington Eq 4. on p. 48 (log formula) fill in • Bevington Eq 4.3 on p. 52, Π should be π . • Bevington Eq 6.10 on p. 105, x should be x i in first line and 1 σ 2 i should be x i σ 2 i in last line. 2 Gaussian Distribution: 2:10 — 2:15, 5 min • p G = 1 √ 2 πσ 2 e − 1 2 ( x x σ ) 2 (1) • Limit of sum of binomial (cointoss) distribution (and most others) for large N • “Normal” distribution • 1 σ = 65% of measurements closer to mean than this • 2 σ = 95% of measurements closer to mean than this • 3 σ = 99% of measurements closer to mean than this • “Wellbehaved” errors follow it • Memorize it! • Not analytically integrable: Find function to calculate integral values. 3 Poisson Distribution: 2:15 — 2:25, 10 min • Timing of random, discrete events in time or space (diagram, don’t confuse x with space!) • Example: Light! • Say there are n events per unit time, on average • Then τ = 1 /n is the average interval between events • In time t we would expect an average of t/τ = tn = N events 1 • The probability of getting x events in time t is P ( x, t ) = ( t/τ ) x x ! e − t/τ = N x x ! e − N (2) • ¯ x = N • σ = √ N • For large N , Poisson approaches a Gaussian with ¯ x = N and σ = √ N • Gaussian, BUT mean and std. dev are locked together! • ¯ x is signal and σ is noise, so S/N = ¯ x σ = N √ N = √ N (3) • Quality of data improves as √ number of counts......
View
Full
Document
This note was uploaded on 11/09/2009 for the course AST 4762 taught by Professor Harrington during the Fall '09 term at University of Central Florida.
 Fall '09
 Harrington
 Astronomical

Click to edit the document details