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Diketahui fungsi distribusi kumulatif suatu variab...

Diketahui fungsi distribusi kumulatif suatu variabel acak kontinu sebagai berikut.

 size 14px F size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px space begin mathsize 14px style open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space x less or equal than 3 end cell row cell fraction numerator x squared minus 6 x plus 9 over denominator 16 end fraction comma space untuk space 3 less than x less or equal than 7 end cell row cell 1 comma space untuk space x greater or equal than 7 end cell end table close end style  

Fungsi distribusi peluang variabel acak begin mathsize 14px style X end style adalah ....

  1. 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 fraction numerator x minus 3 over denominator 8 end fraction comma space untuk space 3 less than x less or equal than 7 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

  2. 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 fraction numerator x minus 3 over denominator 16 end fraction comma space untuk space 3 less than x less or equal than 7 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

  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 fraction numerator x minus 6 over denominator 16 end fraction comma space untuk space 3 less than x less or equal than 7 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

  4. 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 fraction numerator x minus 6 over denominator 8 end fraction comma space untuk space 3 less than x less or equal than 7 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

  5. 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 fraction numerator 2 x minus 3 over denominator 8 end fraction comma space untuk space 3 less than x less or equal than 7 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

Jawaban:

begin mathsize 14px style straight f open parentheses x close parentheses equals fraction numerator straight d over denominator straight d x end fraction straight F open parentheses x close parentheses end style

Pada interval begin mathsize 14px style 3 less than x less or equal than 7 comma space F open parentheses x close parentheses equals fraction numerator x squared minus 6 x plus 9 over denominator 16 end fraction end style, sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses fraction numerator x squared minus 6 x plus 9 over denominator 16 end fraction close parentheses end cell row blank equals cell 1 over 16 fraction numerator straight d over denominator straight d x end fraction open parentheses x squared minus 6 x plus 9 close parentheses end cell row blank equals cell 1 over 16 open parentheses 2 x minus 6 close parentheses end cell row blank equals cell fraction numerator 2 x minus 6 over denominator 16 end fraction end cell row blank equals cell fraction numerator x minus 3 over denominator 8 end fraction end cell end table end style 

Dengan demikian, diperoleh fungsi distribusi peluang variabel acak X:

begin mathsize 14px style f open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator x minus 3 over denominator 8 end fraction comma space untuk space 3 less than x less or equal than 7 end cell row cell 0 comma space untuk space x space yang space lain end cell end table close end style 

jadi, jawaban yang tepat adalah A.

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