discrete & continuous probabilty distributions.pdf
TRANSCRIPT
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Jurusan Teknik IndustriJurusan Teknik Informatika
Fakultas Teknik
Universitas Yudharta Pasuruan
Qomaruddin, M.Si
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PengertianDaftar semua hasil percobaan dan probabilitas masing-masingoutcome.
Contoh.
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Pembahasan.
“zero heads” hanya muncul sekali
“one head” muncul 3x
“two head” muncul 3x
“three heads muncul sekali
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Pengertian
Hasil dari suatu percobaan nilainya berbeda
Bisa berupa diskrit ataupun kontinu
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Variable Diskrit
hasil penghitungan
Contoh.Jumlah mahasiswa masing-masing kelas & jurusan di FakultasTeknik UYP
• TI “A” 40 mhs
• TI “B” 25 mhs
• T. Industri 20 mhs
Variabel Kontinuhasil pengukuran
Contoh
Tinggi badan mahasiswa Teknik Industri, yaitu: 160 cm, 163 cm,165 cm, 168 cm, 170 cm, 175 cm.
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Rata-rata (mean)
= ()
=
()
Varian & Standar Deviasi
Keterangan.
: rata-rata
: varian
: simpangan baku
x : variable acak
P( x) : probabilitas x
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Bagaimana cara menghitung &
menggunakan distribusi probabilitas
Binomial?
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= (1 )−
Bentuk Umum
Keterangan:
P(x) : probabilitas distribusi binomial
C : Combinasi
n : jumlah percobaan
x : jumlah percobaan yg berhasilπ : probabilitas keberhasilan masing-masing percobaan
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Contoh.
Maskapai Penerbangan Air Asia, dari Lima penerbangan pesawat Air
Asia, kemungkinan keterlambatan penerbangan adalah 20%.
a. Berapakah probabilitas tidak ada pesawat yang terbang
terlambat?
b. Berapakah kemungkinan satu penerbangan yang PASTI
terlambat?
Pembahasan
Diketahui
n = 5
π = 0,2
x = 0 . . . . ?
x = 1 . . . . ?
=
(1 )−
0 = 5(0,2) (1 0,2)−
0 = 0,3277
1 = 5(0,2) (1 0,2)−
1 = 0,4096
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=
=(1)
= (1 )
Keterangan.
: rata-rata
: varian
: simpangan baku
n : jumlah percobaan
: probabilitas keberhasilan
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Menjawab Keterbatasan Distribusi
Binomial
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Pengertian
Menggambarkan jumlah waktu pada beberapa kejadian
selama interval tertentu.
Ciri ciri
Distribusi Probabilitas Diskrit
Nilai Probabilitas proporsional dengan ukuran interval
Independent kemunculan pada satu interval tidak
berpengaruh pada interval yang lain
Kemiringannya tidak pernah negatif
Distribusinya bergantung nilai
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Bentuk Umum
= −
! Keterangan.
: rata-rata
: varian
: simpangan baku
x : variable acak
P( x) : probabilitas x
= ()
= ()
Rata-rata (mean)
Varian & Standar Devisasi
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Contoh
Dari 1000 penerbangan suatu maskapai, terdapat 300
bagasi yang hilang.
a. Berapakah probabilitas tidak ada bagasi yang
hilang?
b. Berapakah probabilitas hilang 1 bagasi?
= −!
Pembahasan
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