Expression 5: "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals 100 left parenthesis, 1 minus Start product from "n" equals left parenthesis, 1 minus StartFraction, "S" Over 100 , EndFraction , right parenthesis StartFraction, 100 Over "P" , EndFraction plus 1 minus "x" to left parenthesis, 1 minus StartFraction, "S" Over 100 , EndFraction , right parenthesis StartFraction, 100 Over "P" , EndFraction , end product, StartFraction, "n" Over StartNestedFraction, 100 NestedOver "P" , EndNestedFraction , EndFraction , right parenthesisf1x=1001−1−S100100P∏n=1−S100100P+1−xn100P
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Expression 6: "f" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis equals 100 left parenthesis, 1 minus Start product from "n" equals "S" Subscript, 2 , Baseline "P" Subscript, 2 , Baseline plus 1 minus "x" to "S" Subscript, 2 , Baseline "P" Subscript, 2 , Baseline , end product, StartFraction, "n" Over "P" Subscript, 2 , Baseline , EndFraction , right parenthesisf2x=1001−S2P2∏n=S2P2+1−xnP2
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Expression 7: "f" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesis equals "S" plus "P" "x"f3x=S+Px
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Expression 8: "f" Subscript, 4 , Baseline equals 100 negative left parenthesis, left parenthesis, 100 Start product from "n" equals 1 to "x" , end product, left bracket, 1 minus left parenthesis, StartFraction, "S" Over 100 , EndFraction plus StartFraction, "P" times left parenthesis, "n" minus 1 , right parenthesis Over 100 , EndFraction , right parenthesis , right bracket , right parenthesis , right parenthesisf4=100−100x∏n=11−S100+P·n−1100
