probability distribution of apparent proportions given actual proportions | chi-squared confidence triangle?
distribution apparent in sample (given sample)
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Expression 13: "Q" left parenthesis, "l" , right parenthesis equals left parenthesis, Start sum from "i" Subscript, 1 , Baseline equals 1 to length left parenthesis, "l" , right parenthesis , end sum, left brace, "l" left bracket, "i" Subscript, 1 , Baseline , right bracket equals 0 : 1 , 0 , right brace , Start sum from "i" Subscript, 1 , Baseline equals 1 to length left parenthesis, "l" , right parenthesis , end sum, left brace, "l" left bracket, "i" Subscript, 1 , Baseline , right bracket equals 1 : 1 , 0 , right brace , right parenthesisQl=lengthl∑i1=1li1=0:1,0,lengthl∑i1=1li1=1:1,0
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Expression 14: "L" Subscript, "s" , Baseline to left bracket, "Q" left parenthesis, "C" left parenthesis, random left parenthesis, "n" , right parenthesis , right parenthesis , right parenthesis for "k" equals left bracket, 1... "N" , right bracket , right bracketLs→QCrandomnfork=1...N
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Expression 15: "L" Subscript, "c" , Baseline to left bracket, Start sum from "i" Subscript, 2 , Baseline equals 1 to length left parenthesis, "L" Subscript, "s" , Baseline , right parenthesis , end sum, left brace, distance left parenthesis, "L" Subscript, "s" , Baseline left bracket, "i" Subscript, 2 , Baseline , right bracket , left parenthesis, "P" Subscript, 1 , Baseline , "P" Subscript, 2 , Baseline , right parenthesis , right parenthesis equals 0 : 1 , 0 , right brace for "P" Subscript, 1 , Baseline equals left bracket, 0... "n" , right bracket , "P" Subscript, 2 , Baseline equals left bracket, 0... "n" , right bracket , right bracketLc→lengthLs∑i2=1distanceLsi2,P1,P2=0:1,0forP1=0...n,P2=0...n
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maybe don't open
Hide this folder from students.
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Expression 19: "L" Subscript, "p" , Baseline equals left bracket, StartFraction, left parenthesis, "P" Subscript, 1 , Baseline , "P" Subscript, 2 , Baseline , right parenthesis Over "n" , EndFraction for "P" Subscript, 1 , Baseline equals left bracket, 0... "n" , right bracket , "P" Subscript, 2 , Baseline equals left bracket, 0... "n" , right bracket , right bracketLp=P1,P2nforP1=0...n,P2=0...n
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confidence box?
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Expression 21: "M" left parenthesis, "l" , "j" , right parenthesis equals Start sum from "i" equals negative "j" to "j" , end sum, Start sum from "h" equals negative "j" to "j" , end sum, "L" Subscript, "c" , Baseline left bracket, left parenthesis, "n" plus 1 , right parenthesis floor left parenthesis, "n" "p" Subscript, 2 , Baseline plus "i" , right parenthesis plus floor left parenthesis, "n" "p" Subscript, 1 , Baseline , right parenthesis plus "h" plus 1 , right bracketMl,j=j∑i=−jj∑h=−jLcn+1floornp2+i+floornp1+h+1
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Expression 22: "r" equals 7r=7
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Expression 23: StartFraction, "M" left parenthesis, "L" Subscript, "s" , Baseline , "r" , right parenthesis Over "N" , EndFractionMLs,rN
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Expression 24: StartFraction, "r" Over "n" , EndFractionrn
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"radius" of 95% confidence box in terms of sample size
