STA3032 Week 3 outline
STA3032 Week 3 outline STA3032
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This 2 page Class Notes was uploaded by Tia Belvin on Tuesday February 9, 2016. The Class Notes belongs to STA3032 at University of Florida taught by Demetris Athienitis in Spring 2016. Since its upload, it has received 39 views. For similar materials see Engineering Statistics in Engineering and Tech at University of Florida.
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Date Created: 02/09/16
STA3032 Week 3 2.5.10 COMMON CONTINUOUS DISTRIBUTIONS 1 A uniform random variable places equal weight to all values within its support and is continuous. a A uniform random variable has p.d.f. 1 f x = b−a for a≤x≤b 2 Normal a The normal distribution has parameter µ and a scale parameter σ2 b Normal distribution has p.d.f. −1(x−μ) 1 2σ f(x)= e for -∞<x<∞ σ√2π 2 3 Denoted by X N(μ,σ ) 4 Linear transformations are reversible, we can reverse back with Z values x−μ Z= σ 2.6 CENTRAL LIMIT THEOREM 1 CLT has three versions: classical, Lyapunov, and Linderberg a All say that the asymptotic distribution of the sample mean X is normal σ2 X N(μ, ) for n>30 n i Binomial: np>5 and n(1−p )>5 ii Poisson: λ>10 2.7 NORMAL PROBABILITY PLOT 1 The probability plot is a graphical technique for comparing two data sets, either two empirical, or one empirical and one theoretical. 2 The empirical c.d.f. is the cumulative distribution function associated with the empirical measure of the sample. STA3032 Week 3 F (x) n 3 There are two types of plots used to plot the empirical c.d.f. to the normal theoretical one ( G(x)¿ ^ F a A P-P plot plots (¿¿n (x),G(x)) ¿ FF (¿¿n−1(x),G (x) ) b A Q-Q plot plots the quantile functions ¿
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