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# COMPLETE Statistics Notes - Part 4 (got 4.0 in the course)

4 Pages
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School
Boston College
Department
Economics
Course
ECON 1151
Professor
All
Semester
Spring

Description
Final—Basics, Probability, & Miscellaneous Keely Henesey Population Sample N n Arithmetic Mean μ= 1 x x= 1 x N i=1 i n∑i=1 i 2 1 N 2 2 1 n 2 σ = ∑ (xi−μ ) s = ∑ (xi−x ) N i=1 (n−1)i=1 N N N Variance σ = 1 ∑ (xi−μ)( iμ ) σ = 1 ∑ (xi−μ)xi σ = 1 ∑ xi−μ 2 N i=1 N i=1 N i=1 Alternate formulas can be applied to sample variance but remember… 1. Divide by n−1) 2. Use  x Standard Deviation σ= √ 2 s= √ 2 1 N 1 n Cov(x, y)=σ xy ∑ (xi−μx)(yi−μy) Cov(x, y)=sxy ∑ (xi−́ )(í y) N i=1 n−1 i=1 1 n 1 n sxy n−1 ∑ (i−́x)yi sxy n−1 ∑ (yi−y )i Covariance i=1 i=1 Alternate formulas can be applied to population variance but remember… 1. Divide by  2. Use  μ Cov>1 → IncreasingLinear Relationship { →DecreasingLinear Relationship }   Cov<1 ] ρ = Cov(x, y) r = Cov(x, y) xy σ x y xy sxsy Correlation  [r=1 ]→ Perfectly PositiveLinear Relationship Coefficient [r=0 ]→ NOLinear Relationship [r=−1 ]Perfectly Negative Linear Relationship Relationship∃If …r∣≥ 2 ( √n ¿ 3 If 0 1 ∑x (x−́x) Skewness Skewness= () 3 → Symmetric ] n s If +¿If−¿ → [Right Skewed] → ¿ ] σ s Coefficient of  CV= ×μ00 (if μ>0) CV= ×x́0 (if ́ x>0) Variation A greater CV implies a greater amount of relative fluctuation Final—Basics, Probability, & Miscellaneous Keely Henesey Probability Rules Complement Rule P(A')=1−P(A) Addition Rule P(A∪B)=P(A)+P(B)−P(A∩B) Conditionality Rule P(A ∣B)= P(A∩B) P(B) Multiplication Rule P(A∩B)=P(A ∣B)∙P(B)=P(B ∣A)∙P(A) P(A∩B)=P(A)∙P(B) Statistical Independence P(A B)=P(A) P(B ∣A)=P(B) P A B = P(B ∣A)P(A) P(B) Bayes’ Theorem P(A ∣B)P(B) P(B∨A)= P(A) Bayes’ Theorem II P E A = P ( ∣ i) ( )i ( i ) P ( ∣ 1) ( )1A E(P ∣ 2) ( 2 E P E ( ∣ K) ( )K
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