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Lecture 7

# ECON 2209 Lecture 7: 6February_EconStats_Karagodsky Premium

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School
Department
Economics
Course
ECON 2209
Professor
Karagodsky
Semester
Fall

Description
EconStatistics February 6 2017 1 Recap Coin ipping experiments outcome(i) p(x = xi) x i P(x i (i ) 1 .065 4 .26 2 .25 2 .50 3 .375 0 0 4 .25 0 0 5 .065 10 .65 Total: 1.0 4 .11 E[x] = .11 Question: What if you shift this by 10? Answer: E[10x] = 10E[x] = 1.1 This is called a linear transformation 2 Linear Functions of Random Variables If Y = a + bX then: y= E[a + bx] = a + b x This is important to remember. Not important to know the proof. 3 Variance Will the variance work the same way? outcome(i) p(xi) (i x) p(x i (i x) if x = 10x 1 :065(3:89) 2 :065(3:89) 2 2 2 2 :25(1:89) :25(1:89 10) 3 :375(:11) :375(:11 10) 4 :25(:11)2 :25(:11 10) 2 2 5 :065(10:11) :065(10:11 10) Column Total: 8.528 852.8 Notice that a 10x increase led to a 100x increase in the nal value. This is because the 10x gets squared before being multiplied in. 1
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