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Sebuh bola dilemparkan ke ring basket sebanyak 3 kali. Jika X menyatakan banyak bola masuk ke dalam ring basket, tentukan: b. Distribusi peluang kumulatif variabel acak X dalam bentuk tabel, fungsi dan grafik.

Pertanyaan

Sebuh bola dilemparkan ke ring basket sebanyak 3 kali. Jika X menyatakan banyak bola masuk ke dalam ring basket, tentukan:

b. Distribusi peluang kumulatif variabel acak X dalam bentuk tabel, fungsi dan grafik.

  1. undefined 

  2. size 14px. size 14px. size 14px. size 14px. 

Pembahasan Soal:

Peluang suatu nilai variabel acak binomial dinamakan peluang binomial. Secara umum persamaan peluang binomial x kejadian yang diharapkan dari n percobaan binomial dinyatakan:

begin mathsize 14px style straight P left parenthesis straight X equals straight x right parenthesis equals straight b left parenthesis straight x semicolon straight n semicolon straight p right parenthesis equals straight C presubscript straight n subscript straight x times straight p to the power of straight x times straight q to the power of straight n minus straight x end exponent end style  

begin mathsize 14px style straight n equals 3 comma space straight p equals 1 half comma space straight q equals 1 half straight x equals 0 comma 1 comma 2 comma 3 straight P left parenthesis straight X equals 0 right parenthesis equals straight C presubscript 3 subscript 0 open parentheses 1 half close parentheses to the power of 0 open parentheses 1 half close parentheses cubed equals fraction numerator 3 factorial over denominator 3 factorial times 0 factorial end fraction times 1 times 1 over 8 equals 1 over 8 straight P left parenthesis straight X equals 1 right parenthesis equals straight C presubscript 3 subscript 1 open parentheses 1 half close parentheses to the power of 1 open parentheses 1 half close parentheses squared equals fraction numerator 3 factorial over denominator 2 factorial times 1 factorial end fraction times 1 half times 1 fourth equals fraction numerator 3 times 2 factorial over denominator 2 factorial times 1 end fraction times 1 over 8 equals 3 over 8 straight P open parentheses straight X equals 2 close parentheses equals straight C presubscript 3 subscript 2 open parentheses 1 half close parentheses squared open parentheses 1 half close parentheses to the power of 1 equals fraction numerator 3 factorial over denominator 1 factorial times 2 factorial end fraction times 1 fourth times 1 half equals fraction numerator 3 times 2 factorial over denominator 1 times 2 factorial end fraction times 1 over 8 equals 3 over 8 straight P left parenthesis straight X equals 3 right parenthesis equals straight C presubscript 3 subscript 3 open parentheses 1 half close parentheses cubed open parentheses 1 half close parentheses to the power of 0 equals fraction numerator 3 factorial over denominator 0 factorial times 3 factorial end fraction times 1 over 8 times 1 equals fraction numerator 3 factorial over denominator 1 times 3 factorial end fraction times 1 over 8 equals 1 over 8 end style 

Tabel distribusi peluang variabel acak X adalah 

X=x 0 1 2 3
f(x) begin mathsize 14px style 1 over 8 end style begin mathsize 14px style 3 over 8 end style begin mathsize 14px style 3 over 8 end style begin mathsize 14px style 1 over 8 end style

Tabel distribusi peluang kumulatif variabel acak X adalah 

X=x 0 1 2 3 Jumlah
f(x) undefined undefined undefined undefined begin mathsize 14px style 1 end style

Fungsi distribusi peluang variabel acak X

begin mathsize 14px style f open parentheses x close parentheses equals open curly brackets table row cell 0 comma space untuk space x space yang space lain end cell row cell 1 over 8 comma space x equals 0 comma 3 end cell row cell 3 over 8 comma space x equals 1 comma 2 end cell end table close end style 

Gambar Grafik distribusi peluang variabel acak X

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Maret 2021

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