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

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

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