DISTRIBUSI BINOMIAL BERNOULLI PROCESS The experiment consists of
DISTRIBUSI BINOMIAL
BERNOULLI PROCESS • The experiment consists of n repeated trials. • Each trial results in an outcome that may be classified as a success or a failure. • The probability of success, denoted by p, remains constant from trial to trial. • The repeated trials are independent.
BINOMIAL DISTRIBUTION A Bernoulli trial can result in a success with probability p and a failure with probability q = 1 p. Then the probability distribution of the binomial random variable X, the number of successes in n independent trials, is
CONTOH SOAL DISTRIBUSI BINOMIAL (1) • The probability that a certain kind of component will survive a given shock test is ¾. Find the probability that exactly 2 of the next 4 components tested survive!
CONTOH SOAL DISTRIBUSI BINOMIAL (2) • The probability that a patient recovers from a rare blood disease is 0. 4. If 15 people are known to have contracted this disease, what is the probability that exactly 5 survive?
LATIHAN (1) • Sebuah produsen obat batuk memberikan pernyataan bahwa obat batuknya 90% efektif dalam menyembuhkan penyakit batuk. Apabila 7 orang dengan batuk serupa diberikan obat dari produsen itu, tentukan peluangnya (a) tepat 3 orang di antaranya sembuh (b) tepat 5 orang di antaranya sembuh (c) semuanya sembuh
LATIHAN (2) • Seorang pemain basket memiliki peluang 0, 7 untuk memasukkan bola ke dalam keranjang. Apabila ia melakukan 10 lemparan berturutan, tentukan peluang (a) tepat 6 bola berhasil masuk keranjang (b) tepat 3 bola berhasil masuk keranjang (c) tak kurang dari 8 bola masuk keranjang (d) tak ada bola yang masuk
LATIHAN (3) • In a certain city district the need for money to buy drugs is given as the reason for 75% of all thefts. Find the probability that among the next 8 theft cases reported in this district, (a) exactly 2 resulted from the need for money to buy drugs; (b) at most 3 resulted from the need for money to buy drugs. (c) at least 3 resulted from the need for money to buy drugs.
LATIHAN (4) • A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that more than 2 of the next 9 vehicles are from out of the state?
DISTRIBUSI POISSON
POISSON PROBABILITY EXPERIMENT • The random variable is the number of times some event occurs during a defined interval. • The probability of the event is proportional to the size of the interval. • The intervals do not overlap and are independent.
POISSON DISTRIBUTION • The probability distribution of the Poisson random variable X, representing the number of outcomes occuring in a given time interval or specified region denoted by t, is given by: e 0, 71828
CONTOH SOAL DISTRIBUSI POISSON (1) • Rata-rata banyaknya nasabah yang masuk ke dalam antrian bagian teller suatu bank setiap menitnya adalah 2. Tentukan peluang dalam 1 menit datang 3 nasabah ke dalam antrian bagian teller tersebut!
CONTOH SOAL DISTRIBUSI POISSON (2) Seorang sekretaris rata-rata menerima panggilan telepon sebanyak 3 buah dalam setiap 20 menit. Tentukan peluang dalam 1 jam berikutnya ia menerima 7 buah panggilan telepon. Jawab: λ = 0, 15/menit, t = 60 menit λt = 0, 15. 60 = 9
CONTOH SOAL DISTRIBUSI POISSON (3) • Banyaknya kata yang salah ejaan dalam suatu surat kabar adalah 3 dalam tiap 4 halaman. Tentukan peluang dalam 10 halaman surat kabar tersebut terdapat kurang dari 4 kata salah ejaan. • λ = 0, 75/halaman t = 10 halaman λt = 0, 75. 10 = 7, 5 • P[X<4] = p(0; 7, 5) + p(1; 7, 5) + p(2; 7, 5) + p(3; 7, 5) = 0, 0006 + 0, 0041 + 0, 0156 + 0, 0389 = 0, 0592.
CONTOH SOAL DISTRIBUSI POISSON (4) • Pada contoh soal sebelumnya, tentukan peluang dalam 10 halaman surat kabar tersebut terdapat lebih dari 3 kata salah ejaan. • P[X>3] = p(4; 7, 5) + p(5; 7, 5) + p(6; 7, 5) + p(7; 7, 5) +. . . = 1 – [p(0; 7, 5) + p(1; 7, 5) + p(2; 7, 5) + p(3; 7, 5)] = 1 – 0, 0592 = 0, 9408.
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