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Suatu variabel acak kontinu   memiliki fungsi dist...

Suatu variabel acak kontinu begin mathsize 14px style X end style  memiliki fungsi distribusi peluang berikut.

begin mathsize 14px style f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 8 minus x over denominator 8 end fraction comma space untuk space 4 less or equal than x less or equal than 8 end cell row cell 0 comma space space space space space space space space space untuk space x space yang space lain end cell end table close end style  

Fungsi distribusi kumulatif variabel acak undefined  adalah ....

  1. begin mathsize 14px style F left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space x less than 4 end cell row cell negative fraction numerator x squared minus 16 x plus 48 over denominator 8 end fraction comma space untuk space 4 less or equal than x less than 8 end cell row cell 1 comma space untuk space x greater or equal than 8 end cell end table close end style 

  2. begin mathsize 14px style F left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space x less than 4 end cell row cell negative fraction numerator x squared minus 8 x plus 48 over denominator 8 end fraction comma space untuk space 4 less or equal than x less than 8 end cell row cell 1 comma space untuk space x greater or equal than 8 end cell end table close end style 

  3. size 14px F size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals begin mathsize 14px style open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space x less than 4 end cell row cell negative fraction numerator x squared minus 16 x minus 48 over denominator 16 end fraction comma space untuk space 4 less or equal than x less than 8 end cell row cell 1 comma space untuk space x greater or equal than 8 end cell end table close end style  

  4. size 14px F size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals begin mathsize 14px style space open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space x less than 4 end cell row cell negative fraction numerator x squared minus 16 x plus 48 over denominator 16 end fraction comma space untuk space 4 less or equal than x less than 8 end cell row cell 1 comma space untuk space x greater or equal than 8 end cell end table close end style   

  5. size 14px F size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals begin mathsize 14px style space open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space x less than 4 end cell row cell negative fraction numerator x squared plus 16 x plus 48 over denominator 16 end fraction comma space untuk space 4 less or equal than x less than 8 end cell row cell 1 comma space untuk space x greater or equal than 8 end cell end table close end style  

Jawaban:

Variabel acak X terdefinisi pada interval begin mathsize 14px style 4 less or equal than x less than 8 end style.

Fungsi distribusi kumulatif variabel acak X:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell F open parentheses t close parentheses end cell equals cell P open parentheses X less or equal than t close parentheses end cell row blank equals cell integral subscript 4 superscript t f open parentheses x close parentheses d x end cell row blank equals cell integral subscript 4 superscript t open parentheses fraction numerator 8 minus x over denominator 8 end fraction close parentheses d x end cell row blank equals cell 1 over 8 open square brackets 8 x minus 1 half x squared close square brackets subscript 4 superscript t end cell row blank equals cell 1 over 8 open square brackets open parentheses 8 open parentheses t close parentheses minus 1 half open parentheses t close parentheses squared close parentheses minus open parentheses 8 open parentheses 4 close parentheses minus 1 half open parentheses 4 close parentheses squared close parentheses close square brackets end cell row blank equals cell 1 over 8 open parentheses 8 t minus 1 half t squared minus 24 close parentheses end cell row blank equals cell t minus 1 over 16 t squared minus 3 end cell row blank equals cell negative 1 over 16 t squared plus t minus 3 end cell row blank equals cell negative fraction numerator t squared minus 16 t plus 48 over denominator 16 end fraction end cell end table end style 

Jadi, fungsi distribusi kumulatif variabel acak X adalah

begin mathsize 14px style F open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space x less than 4 end cell row cell negative fraction numerator x squared minus 16 x plus 48 over denominator 16 end fraction comma space untuk space 4 less or equal than x less than 8 end cell row cell 1 comma space untuk space x greater or equal than 8 end cell end table close end style 

Jadi, jawaban yang tepat adalah D.

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