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Pertanyaan

Diketahui suatu variabel acak X dengan . Nilai dari P(X = 6) – P(X = 7) adalah ....

Diketahui suatu variabel acak X dengan begin mathsize 14px style X tilde b open parentheses 8 comma 1 fourth close parentheses end style.

Nilai dari P(X = 6) – P(X = 7) adalah ....

  1. begin mathsize 14px style 57 over 4 to the power of 7 end style 

  2. begin mathsize 14px style 69 over 4 to the power of 7 end style 

  3. begin mathsize 14px style 315 over 4 to the power of 7 end style 

  4. begin mathsize 14px style 57 over 4 to the power of 8 end style 

  5. begin mathsize 14px style 69 over 4 to the power of 8 end style 

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P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

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Pembahasan

Perhatikan bahwa variabel acak X berdistribusi binomial dengan n = 8 dan . Sehingga didapat Maka Sehingga dan Sehingga

Perhatikan bahwa variabel acak X berdistribusi binomial dengan n = 8 dan begin mathsize 14px style p equals 1 fourth end style.

Sehingga didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row q equals cell 1 minus p end cell row blank equals cell 1 minus 1 fourth end cell row blank equals cell 3 over 4 end cell end table end style

Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses X equals x close parentheses end cell equals cell C presubscript n presuperscript blank subscript x times p to the power of x times q to the power of n minus x end exponent end cell row blank equals cell C presubscript 8 presuperscript blank subscript x times open parentheses 1 fourth close parentheses to the power of x times open parentheses 3 over 4 close parentheses to the power of 8 minus x end exponent end cell end table end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses X equals 6 close parentheses end cell equals cell C presubscript 8 presuperscript blank subscript 6 times open parentheses 1 fourth close parentheses to the power of 6 times open parentheses 3 over 4 close parentheses to the power of 8 minus 6 end exponent end cell row blank equals cell fraction numerator 8 factorial over denominator open parentheses 8 minus 6 close parentheses factorial times 6 factorial end fraction times open parentheses 1 fourth close parentheses to the power of 6 times open parentheses 3 over 4 close parentheses squared end cell row blank equals cell fraction numerator 8 times 7 times 6 factorial over denominator 2 factorial times 6 factorial end fraction times 1 over 4 to the power of 6 times 9 over 4 squared end cell row blank equals cell fraction numerator 8 times 7 over denominator 2 times 1 end fraction times 1 over 4 to the power of 6 times 9 over 4 squared end cell row blank equals cell fraction numerator 4 times 7 over denominator 1 end fraction times 1 over 4 to the power of 6 times 9 over 4 squared end cell row blank equals cell 7 over 1 times 1 over 4 to the power of 5 times 9 over 4 squared end cell row blank equals cell 63 over 4 to the power of 7 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses X equals 7 close parentheses end cell equals cell C presubscript 8 presuperscript blank subscript 7 times open parentheses 1 fourth close parentheses to the power of 7 times open parentheses 3 over 4 close parentheses to the power of 8 minus 7 end exponent end cell row blank equals cell fraction numerator 8 factorial over denominator open parentheses 8 minus 7 close parentheses factorial times 7 factorial end fraction times open parentheses 1 fourth close parentheses to the power of 7 times open parentheses 3 over 4 close parentheses to the power of 1 end cell row blank equals cell fraction numerator 8 times 7 factorial over denominator 1 factorial times 7 factorial end fraction times 1 over 4 to the power of 7 times 3 over 4 end cell row blank equals cell 8 over 1 times 1 over 4 to the power of 7 times 3 over 4 end cell row blank equals cell 2 over 1 times 1 over 4 to the power of 7 times 3 over 1 end cell row blank equals cell 6 over 4 to the power of 7 end cell end table end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses X equals 6 close parentheses minus P open parentheses X equals 7 close parentheses end cell equals cell 63 over 4 to the power of 7 minus 6 over 4 to the power of 7 end cell row blank equals cell 57 over 4 to the power of 7 end cell end table end style 

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