NATS 1500 Chapter Notes - Chapter 1-7: Variance, Standard Deviation

• School: York University
• Department: Natural Science
• Course: NATS 1500
• Professor: Georges Monette

Document Summary

Descriptive statistics: given a srs x1, x2, , xn: sample mean: X = (cid:80)n i=1 xi n: sample variance: (cid:80)n (cid:0)xi x(cid:1)2. S2 = i=1 n 1 or s2 = (cid:80)n i=1 x 2 i n( x)2 n 1 or s2 = (cid:20)(cid:80)n i=1 x 2 i=1 xi)2 n i ((cid:80)n n 1 (cid:21) Xk fk: the sample size: n =(cid:80)k, sample mean: i=1 fi , sample variance: X = (cid:80)k n i n( x)2 i=1 fi x 2 n 1. P (a b) = p (a)p (b), a,b independent. P (a b) = p (a) + p (b) p (a b) 2 = v ar(x) =(cid:80) x s xp (x = x) x s(x )2p (x = x) = e(x 2) (e(x))2: transforming variables. V ar(ax) = a2v ar(x: binomial trials. P (x = x) =(cid:0)n (cid:0)n (cid:1) = n! (n x)!x! (cid:1)px(1 p)n x x x.