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Mata Kuliah : K0194-Pemodelan Matematika Terapan Tahun : 2008

Mata Kuliah : K0194-Pemodelan Matematika Terapan Tahun : 2008. Model MARKOV Pertemuan 21:. Learning Outcomes. Mahasiswa akan dapat menjelaskan pengertian dan mengerjakan masalah markov dalam berbagai contoh aplikasi. Outline Materi:. Pengertian Analisis Markov Karakteristik Markov

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Mata Kuliah : K0194-Pemodelan Matematika Terapan Tahun : 2008

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  1. Mata Kuliah : K0194-Pemodelan Matematika TerapanTahun : 2008 Model MARKOV Pertemuan 21:

  2. Learning Outcomes • Mahasiswa akan dapat menjelaskan pengertian dan mengerjakan masalah markov dalam berbagai contoh aplikasi..

  3. Outline Materi: • Pengertian Analisis Markov • Karakteristik Markov • Pengambilan Keputusan Markov • Contoh penerapan

  4. Pengertian • Analisis Markov adalah suatu cara menganalisis perangai beberapa variabel yang sedang beredar dalam usaha menduga perangai mendatang dari variabel yang sama. • Analisis Markov telah digunakan dengan berhasil terhadap berbagai macam situasi keputusan antara lain penyelidikan dan dugaan terhadap perangai konsumen perihal kesetia-annya terhadap “merk” tertentu dan peralihan mereka dari satu merk ke merk lainnya, perubahan sikap pelanggan dari “pembayaran lang-sung” ke pembayaran terlambat 30 hari “atau” pembayaran terlambat 60 hari “hingga” hutang buruk/kredit macet.

  5. Proses Markov Adapun proses model rantai Markov, dapat dilakukan dengan langkah-langkah : • Menyusun Matriks Probabilitas Transisi Probabilitas transisi adalah proba-bilitas suatu merk tertentu (atau penjual) akan tetap menguasai para pelanggannya. • Menghitung kemungkinan Market Share di waktu yang akan datang Perhitungan market share di periode waktu kedua dapat diperoleh dengan mengalikan martiks probabilitas transisi dengan market share pada periode pertama. • Menentukan Kondisi Equilibrium Kondisi equilibrium tercapai bila tidak ada pesaing yang mengubah matriks probabilitas transisi. Peng-gunaan matriks probabilitas transisi dapat menggambarkan kondisi-kon-disi equilibrium.

  6. A Markov Chain is a mathematical model for a process which moves step by step through various states. In a Markov chain, the probability that the process moves from any given state to any other particular state is always the same, regardless of the history of the process. A Markov chain consists of states and transitionprobabilities

  7. . Each transition probability is the probability of moving from one state to another in one step. The transition probabilities are independent of the past, and depend only on the two states involved. The matrix of transition probabilities is called the transition matrix.

  8. 0 1 2 3 4 P(Homer wins) = .4 P(Homer loses) = .6 Homer and Marge both start with $2

  9. If Pis the transition matrix for a Markov Chain, then the nth power of P gives the probabilities of going from state to state in exactly n steps.

  10. If the vector v represents the initial state, then the probabilities of winding up in the various states in exactly n steps are exactly v times the nth power of P .

  11. When they both start with $2, the probability that Homer is ruined is 9/13. If Homer starts with $ x and Marge starts with $ N-x, and P(Homer wins) = p, P(Homer loses) = q, then the probability Homer is ruined is

  12. Suppose you be on red in roulette. P(win) = 18/38 = 9/19; P(lose) = 10/19. Suppose you and the house each have $10 Now suppose you have $ 10 and the house has $20

  13. Now suppose you and the house each have $100.

  14. Terima Kasih Semoga berhasil

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