Expression 7: "P" left parenthesis, "x" , "y" , right parenthesis equals 1 half Start sum from "i" equals 1 to 4, end sum, StartFraction, 1 Over 2 Superscript, "i" , Baseline , EndFraction "p" left parenthesis, 2 Superscript, "i" , Baseline times "x" , 2 Superscript, "i" , Baseline times "y" , right parenthesisPx,y=124∑i=112ip2i·x,2i·y
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Expression 8: 1 greater than 0 left brace, "P" left parenthesis, "x" , "y" , right parenthesis less than or equal to 0.1 times left parenthesis, 2 StartFraction, left bracket, 0 , ... , 3 , right bracket Over 3 , EndFraction minus 1 , right parenthesis , right brace1>0Px,y≤0.1·20,...,33−1
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Expression 9: "H" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals "H" left parenthesis, "x" , 0 , right parenthesis left bracket, 1 , right bracketH1x=Hx,01
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Expression 10: "P" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals left parenthesis, "H" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis times "f" left parenthesis, "x" , right parenthesis , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, negative "x" , right parenthesis plus left parenthesis, "H" Subscript, 1 , Baseline left parenthesis, "x" plus 1 , right parenthesis times negative "f" left parenthesis, negative "x" , right parenthesis , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesisP1x=H1x·fxf3−x+H1x+1·−f−xf3x
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Expression 11: "P" Subscript, 1 "b" , Baseline left parenthesis, "x" , right parenthesis equals "H" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, negative "x" , right parenthesis plus "H" Subscript, 1 , Baseline left parenthesis, "x" plus 1 , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesisP1bx=H1xf3−x+H1x+1f3x
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Expression 12: "y" equals "P" left parenthesis, "x" , 0 plus "t" , right parenthesisy=Px,0+t