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PDF of the beta distribution

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Expression 7: "f" left parenthesis, "x" , right parenthesis equals StartFraction, left parenthesis, "x" , right parenthesis Superscript, alpha minus 1 , Baseline left parenthesis, 1 minus left parenthesis, "x" , right parenthesis , right parenthesis Superscript, beta minus 1 , Baseline Over StartNestedFraction, left parenthesis, alpha minus 1 , right parenthesis ! left parenthesis, beta minus 1 , right parenthesis ! NestedOver left parenthesis, alpha plus beta minus 1 , right parenthesis ! , EndNestedFraction , EndFraction left brace, 0 less than "x" less than 1 , right brace

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Expression 8: 0 less than or equal to "y" less than or equal to "f" left parenthesis, "x" , right parenthesis left brace, "x" less than 1 , right brace

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Trigonometry: Period and Amplitude

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