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Lecture 17

# AMS 5 Lecture 17: Class 17 - Random Samples Premium

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Department
Applied Math and Statistics
Course
AMS 5
Professor
Yonatan Katznelson
Semester
Spring

Description
AMS 5 Lecture 17 5152017 (8:009:05) WarmUp: PreCalculus ARWR = At Random, With Replacement Fact: x(1x) <= for all x o Quadratic function, opening down o Xintercepts: 0, 1 o [0][1] Box o Draw n tickets ARWR (at random with replacement) o EV(Sum) = n*Avg(box) = n*(proportion of [1]s in box) = n*p p is in between 0 and 1 o Sum = [1]s are obscure EV( of [1]s) = n*p o SE(Sum) = n 12* SD(box) = n 12* (p(1p))12 EV( of [1]s) = ? o EV([1]s)n*100 = npn*100 = p*100 = of [1]s in box SE( of [1]s) = ? o draw n tickets, will probably see: : EV( of [1]s) + SE( [1]s) : (EV( of [1]s) + SE( [1]s))n*100 12 12 12 12 = ( of [1]s in box) + (n *(p(1p)) )(n * n ) * 100 = p*100 + (p(1p)) n2 12* 100 SE() = (p(1p)) n2 1* 100 Observation: SE() <= 50n 12because (p(1p)) 1* 100 <= 50 for any P. Example: 400 tickets are drawn ARWR from a box with 40[1]s and 60[0]s o p = 40100 = .4 (proportion of [1]s) of [1]s in box = 40 o EV() = 40 o SE() = (.4*.6) 4002 1* 100 = 2.45 When drawing 400 tickets from this box, expect to observe:
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