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Diketahui fungsi peluang f(x) sebagai berikut. f(x)={122x+1​; untuk 0≤x≤30; untuk x yang lain​  Nilai P(X>2)=....

Pertanyaan

Diketahui fungsi peluang f left parenthesis x right parenthesis sebagai berikut.

f italic left parenthesis x italic right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 2 x plus 1 over denominator 12 end fraction semicolon space untuk space 0 less or equal than x less or equal than 3 end cell row cell 0 semicolon space untuk space x space yang space lain end cell end table close 

Nilai straight P left parenthesis X greater than 2 right parenthesis equals.... 

  1. 1 over 6  

  2. 1 third 

  3. 1 half 

  4. 2 over 3 

  5. 5 over 6 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah C.

Karena fungsi peluang terdefinisi untuk variabel acak 0 less or equal than x less or equal than 3, maka straight P left parenthesis X greater than 2 right parenthesis equals straight P left parenthesis 2 less than X less or equal than 3 right parenthesis.

Ingat bahwa table attributes columnalign right center left columnspacing 0px end attributes row cell straight P italic left parenthesis c end cell less than cell X less than d right parenthesis equals integral subscript c superscript d f left parenthesis x right parenthesis d x end cell end table.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight P left parenthesis 2 end cell less than cell X less or equal than 3 right parenthesis equals integral subscript 2 superscript 3 fraction numerator 2 x plus 1 over denominator 12 end fraction d x end cell row cell straight P left parenthesis 2 end cell less than cell X less or equal than 3 right parenthesis equals integral subscript 2 superscript 3 2 over 12 x plus 1 over 12 d x end cell row cell straight P left parenthesis 2 end cell less than cell X less or equal than 3 right parenthesis equals open square brackets fraction numerator up diagonal strike 2 over denominator 12 end fraction times fraction numerator 1 over denominator up diagonal strike 2 end fraction x squared plus 1 over 12 x close square brackets subscript 2 superscript 3 end cell row cell straight P left parenthesis 2 end cell less than cell X less or equal than 3 right parenthesis equals open square brackets 1 over 12 x squared plus 1 over 12 x close square brackets subscript 2 superscript 3 end cell row cell straight P left parenthesis 2 end cell less than cell X less or equal than 3 right parenthesis equals open square brackets open parentheses 1 over 12 open parentheses 3 close parentheses squared plus 1 over 12 open parentheses 3 close parentheses close parentheses minus open parentheses 1 over 12 left parenthesis 2 right parenthesis squared plus fraction numerator 1 over denominator 12 end fraction left parenthesis 2 right parenthesis close parentheses close square brackets end cell row cell straight P left parenthesis 2 end cell less than cell X less or equal than 3 right parenthesis equals open square brackets open parentheses 9 over 12 plus 3 over 12 close parentheses minus open parentheses 4 over 12 plus 2 over 12 close parentheses close square brackets end cell row cell straight P left parenthesis 2 end cell less than cell X less or equal than 3 right parenthesis equals open square brackets 12 over 12 minus 6 over 12 close square brackets equals 6 over 12 equals 1 half end cell end table 

Oleh karena itu, jawaban yang benar adalah C.

96

4.7 (7 rating)

Pertanyaan serupa

Diketahui fungsi peluang f(x)=121​ terdefinisi untuk variabel acak X={x∣−7<x<5, x bilangan riil}. tentukan nilai peluang berikut! b. P(−3<X<1)

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