STA 106 Study Guide - Final Guide: Linear Combination, Normal Distribution, Standard Deviation
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, yn be rvs denoting all possible values of a random sample of size n. Theoretical results: x yi = sample total, if y1, . Yn are independent, then: let y = Ehx yii = e [total] = e [y1 + y2 + + yn] = e [y1] + e [y2] + + e [yn] 2hx yii = 2 [y1 + + yn] = 2 [y1] + + 2 [yn] E(cid:2)y(cid:3) = e(cid:20) 1 nx yi(cid:21) nx e [yi] Now suppose yi"s are drawn from a population with mean y , stdev y . (i. e. e [yi] = y , If y = a + by , y = a + b y , 2. If y n ( y , y ), then y n (a + b y , y = |b| y ) Linear combinations of normal rvs are also normal.
