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Jika variabel acak , nilai  adalah ....

Pertanyaan

Jika variabel acak begin mathsize 14px style straight Z tilde straight N open parentheses 0 comma space 1 close parentheses end style, nilai begin mathsize 14px style straight P open parentheses straight Z less or equal than 3 close parentheses end style adalah ....

  1. begin mathsize 14px style integral subscript 0 superscript 3 fraction numerator 1 over denominator square root of 2 straight pi end root end fraction straight e to the power of negative 1 half z squared end exponent d z end style  begin mathsize 14px style space space space end style 

  2. begin mathsize 14px style integral subscript 2 superscript infinity fraction numerator 1 over denominator square root of 2 straight pi end root end fraction straight e to the power of negative 1 half z squared end exponent d z end style     

  3. begin mathsize 14px style integral subscript negative infinity end subscript superscript 3 fraction numerator 1 over denominator square root of 2 straight pi end root end fraction straight e to the power of negative 1 half z squared end exponent d z end style    begin mathsize 14px style space space space end style 

  4. begin mathsize 14px style integral subscript 0 superscript 3 fraction numerator 1 over denominator straight sigma square root of 2 straight pi end root end fraction straight e to the power of negative 1 half open parentheses fraction numerator x minus straight mu over denominator straight sigma end fraction close parentheses squared end exponent d z end style   begin mathsize 14px style space space space end style 

  5. begin mathsize 14px style integral subscript negative infinity end subscript superscript 3 fraction numerator 1 over denominator straight sigma square root of 2 straight pi end root end fraction straight e to the power of negative 1 half open parentheses fraction numerator x minus straight mu over denominator straight sigma end fraction close parentheses squared end exponent d z end style     

Pembahasan Soal:

Fungsi distribusi kumulatif variabel acak begin mathsize 14px style straight Z tilde straight N open parentheses 0 comma space 1 close parentheses end style didefinisikan sebagai berikut:

begin mathsize 14px style straight P open parentheses straight Z less or equal than z close parentheses equals integral subscript negative infinity end subscript superscript straight z fraction numerator 1 over denominator square root of 2 straight pi end root end fraction straight e to the power of negative 1 half z squared end exponent d z end style 

Sehingga nilai begin mathsize 14px style straight P open parentheses straight Z less or equal than 3 close parentheses end style dari variabel acak begin mathsize 14px style straight Z tilde straight N open parentheses 0 comma space 1 close parentheses end style, sehingga diperoleh:

begin mathsize 14px style straight P left parenthesis straight Z less or equal than 3 right parenthesis equals integral subscript negative infinity end subscript superscript 3 fraction numerator 1 over denominator square root of 2 straight pi end root end fraction straight e to the power of negative 1 half z squared end exponent d z end style  

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Februari 2021

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