18.05 Study Guide - Midterm Guide: Mit Opencourseware
Document Summary
Problem 1. (20 pts: 4,4,4,8) (a) (produced by counting reboots) C pc = 1 (b) from the table: e(c) = 0 + 1 = 6 (c) we use the formula cov(c, r) = e(cr) e(c)e(r). E(cr) = 2 + 3 = cov(c, r) = 1 = . Since covariance is not zero, they are not independent. The negative covariance suggests that as c increases r tends to decrease. Pc users have to reboot less often than mac users. W (d) (i) independendent joint pmf = product of marginal pmf"s. 3 (ii) p (w > m ) = sum of red prob. in table = + + = 8 (iii) cor(w, m ) = 0 since they are independent. The algebraic properties of covariance say that cov(ax + b, cy + d) = accov(x, y ). (t, s) = (x, y ) = 0. 8 , since correlation is scale and shift invariant.
