probability distribution of apparent proportions given actual proportions | chi-squared confidence triangle?

distribution apparent in sample (given sample)

Espressione 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 parenthesis

Espressione 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 bracket

Espressione 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 bracket

maybe don't open

Espressione 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 bracket

confidence box?

Espressione 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 bracket

Espressione 22: "r" equals 7

Espressione 23: StartFraction, "M" left parenthesis, "L" Subscript, "s" , Baseline , "r" , right parenthesis Over "N" , EndFraction

Espressione 24: StartFraction, "r" Over "n" , EndFraction

"radius" of 95% confidence box in terms of sample size

"x" Subscript, 3 , Baseline	"y" Subscript, 3 , Baseline
1		r1c3:
2		r2c3:
5		r3c3:
10	0.3	r4c3:
20	0.2 2	r5c3:
30	0.1 7	r6c3:
40	0.1 5	r7c3:
50	0.1 4	r8c3:
80		r9c3:
100		r10c3:
		r11c3:

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