STAT 2040 Study Guide - Final Guide: Random Variable, Linear Map, Standard Deviation

• School: University of Guelph
• Department: Statistics
• Course: STAT 2040
• Professor: Gary Umphrey

Document Summary

If we transform the data using the linear transformation x = a + bx: X = a + b x, sx = |b|sx, s2. Equivalent alternative formula: s2 = x = b2s2 x s (cid:80) x2 i (p xi)2 n n 1. P (a b) = p (a) + p (b) p (a b). P (a b) = p (a)p (b|a) = p (b)p (a|b). The conditional probability of a, given b has occurred is p (a|b) = p (a b) Two events a and b are independent if and only if: P (a|b) = p (a), p (b|a) = p (b), p (a b) = p (a)p (b). E(x) = =(cid:80) xp(x), 2 = e[(x )2] =(cid:80) (x )2p(x). Expected value and variance of a discrete random variable. E(a + bx) = a + be(x), 2. If x and y are two random variables then e(x + y ) = e(x) + e(y ).