lect09 - UCF Physics AST 5765/4762(Advanced Astronomical...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: UCF Physics: AST 5765/4762: (Advanced) Astronomical Data Analysis Fall 2009 Lecture Notes: 9. Probability Distributions and Error Analysis 1 Check In: 12:30 — 12:40, 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. • HW4 first “real” HW: exercises teach data analysis. • First quiz Thursday. 2 Probability Basics: (Reference) • Description of behavior of many identical, independently-prepared systems • Discrete vs. continuous probability: coin vs. time interval • In the limit of large N , everything appears continuous. • Described by probability density function (PDF) that integrates to 1. • Do definite integral over range to get probability: P ( x in range a − b ) = integraldisplay b a p ( x ) dx (1) integraldisplay ∞-∞ p ( x ) dx = 1 (2) • mean : ¯ x = integraltext ∞-∞ xp ( x ) dx • median : P ( x < median ) = P ( x > median ) = 1 / 2 • mode : max( p ( x )) • variance : σ 2 = integraldisplay ∞-∞ ( x − ¯ x ) 2 p ( x ) dx (3) • mean is also the expected value of x = ( x ) • variance is the expected value of ( x − μ ) 2 , the square of the deviations from the mean 1 • standard deviation : σ • population : all possible measurements of a system, proportionally represented (often infi- nite in number) • draw : one measurement of system • sample : a set of draws • estimate mean, std. dev., etc. from samplemean, std....
View Full Document

{[ snackBarMessage ]}

Page1 / 5

lect09 - UCF Physics AST 5765/4762(Advanced Astronomical...

This preview shows document pages 1 - 3. Sign up to view the full document.

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