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Suatu variabel acak kontinu  memiliki fungsi pelua...

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

begin mathsize 14px style f open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 4 minus straight x over denominator 2 end fraction comma space untuk space 2 less or equal than straight x less than 4 end cell row cell 0 comma space untuk space straight x space yang space lain end cell end table close end style 

Fungsi peluang kumulatif variabel acak X adalah ....

Jawaban:

untuk interval begin mathsize 14px style 2 less or equal than x less than 4 end style, misalkan batas atasnya begin mathsize 14px style p end style, maka:

begin mathsize 14px style F open parentheses p close parentheses equals integral subscript 2 superscript p fraction numerator 4 minus x over denominator 2 end fraction d x F open parentheses p close parentheses equals integral subscript 2 superscript p open parentheses 2 minus 1 half x close parentheses d x F open parentheses p close parentheses equals open square brackets 2 x minus 1 fourth x squared close square brackets subscript 2 superscript p F open parentheses p close parentheses equals open square brackets 2 open parentheses p close parentheses minus 1 fourth open parentheses p close parentheses squared close square brackets minus open square brackets 2 open parentheses 2 close parentheses minus 1 fourth open parentheses 2 close parentheses squared close square brackets F open parentheses p close parentheses equals open square brackets 2 p minus 1 fourth p squared close square brackets minus open square brackets 4 minus 1 close square brackets F open parentheses p close parentheses equals 2 p minus 1 fourth p squared minus 3 F open parentheses p close parentheses equals negative 1 fourth p squared plus 2 p minus 3 F open parentheses x close parentheses equals negative 1 fourth x squared plus 2 x minus 3 end style 

Jadi, fungsi peluang kumulatif variabel acak X adalah:

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