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Diketahui fungsi distribusi peluang suatu variabel...

Diketahui fungsi distribusi peluang suatu variabel acak kontinu sebagai berikut.

begin mathsize 14px style f left parenthesis z right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 24 minus 2 z over denominator 64 end fraction comma space untuk space k less or equal than z less than 12 end cell row cell 0 comma space untuk space straight z space yang space lain end cell end table space close end style

Nilai k adalah...

 

  1. begin mathsize 14px style space end style

  2. begin mathsize 14px style space end stylebegin mathsize 14px style space end style

  3. begin mathsize 14px style space end stylebegin mathsize 14px style space end style

  4. begin mathsize 14px style space end stylebegin mathsize 14px style space end style

  5. 7begin mathsize 14px style space end style begin mathsize 14px style space end style

Jawaban:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript k superscript 12 fraction numerator 24 minus 2 z over denominator 64 end fraction d z end cell equals 1 row cell 1 over 64 cross times open square brackets 24 z minus z squared vertical line subscript k superscript 12 close square brackets end cell equals 1 row cell 24 z minus z squared vertical line subscript k superscript 12 end cell equals 64 row cell open parentheses 24 open parentheses 12 close parentheses minus open parentheses 12 close parentheses squared close parentheses minus open parentheses 24 k minus k squared close parentheses end cell equals 64 row cell 288 minus 144 minus 24 k plus k squared end cell equals 64 row cell k squared minus 24 k plus 144 end cell equals 64 row cell k squared minus 24 k plus 144 minus 64 end cell equals 0 row cell k squared minus 24 k plus 80 end cell equals 0 row cell open parentheses k minus 20 close parentheses open parentheses k minus 4 close parentheses end cell equals 0 row blank blank cell k equals 20 space atau space k equals 4 end cell end table end style   

Jadi, jawaban yang tepat adalah B

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