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Suatu variabel acak kontinu  memiliki fungsi ditri...

Suatu variabel acak kontinu begin mathsize 14px style Z end style memiliki fungsi ditribusi peluang sebagai berikut.

begin mathsize 14px style f left parenthesis z right parenthesis equals open curly brackets table attributes columnalign center end attributes row cell 0 comma space u n t u k space y a n g space l a i n end cell row cell fraction numerator 4 minus z over denominator 8 end fraction comma space u n t u k space 0 less than z less-than or slanted equal to 4 end cell end table close end style 

Tentukan nilai begin mathsize 14px style P open parentheses open vertical bar Z minus 2 close vertical bar less or equal than 1 close parentheses end style!

Jawaban:

nilai begin mathsize 14px style P open parentheses open vertical bar Z minus 2 close vertical bar less or equal than 1 close parentheses end style 

size 14px P begin mathsize 14px style left parenthesis open vertical bar Z minus 2 close vertical bar less or equal than 1 right parenthesis end style size 14px equals size 14px P begin mathsize 14px style left parenthesis negative 1 less or equal than open vertical bar Z minus 2 close vertical bar less or equal than 1 right parenthesis end style size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px P size 14px left parenthesis size 14px 1 size 14px less or equal than size 14px Z size 14px less or equal than size 14px 3 size 14px right parenthesis size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px f begin mathsize 14px style left parenthesis 1 right parenthesis end style size 14px minus size 14px f begin mathsize 14px style left parenthesis 3 right parenthesis end style size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals fraction numerator size 14px 4 size 14px minus size 14px 1 over denominator size 14px 8 end fraction size 14px minus fraction numerator size 14px 4 size 14px minus size 14px 3 over denominator size 14px 8 end fraction size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 3 over size 14px 8 size 14px minus size 14px 1 over size 14px 8 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 2 over size 14px 8 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 1 over size 14px 4   size 14px space size 14px space size 14px space size 14px space size 14px space  

Jadi, nilai begin mathsize 14px style P open parentheses open vertical bar Z minus 2 close vertical bar less or equal than 1 close parentheses end style adalah begin mathsize 14px style 1 fourth end style 

 

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