SATUAN ACARA PERKULIAHAN PROGRAM STUDI MAGISTER TEKNIK ELEKTRO PROGRAM PASCASARJANA

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1 Mata Kuliah/Sks/Smt : Matematika Terapan/ / Tujuan Umum Mata Kuliah :. Mahasiswa memahami konsep-konsep statistika 2. Mahasiswa mampu menerapkan konsep dan alat bantu statistika pada masalah telekomunikasi Tujuan Khusus Mata Kuliah :. Mahasiswa memahami esensi statistika dan probabilitas di aplikasi telekomunikasi 2. Mahasiswa memahami variabel random diskret dan kontinyus, besaran karakteristik dan penggunaannya. Mahasiswa memahami variabel random jamak, karakteristik dan pemakainannya di telekomunikasi 4. Mahasiswa memahami proses random: Gauss, Poisson dsb. 5. Mahasiswa memahami konsep pada Markov chain dan aplikasinya di telekomunikasi 6. Mahasiswa memahami konsep Power Spectral Density di telekomunikasi 7. Mahasiswa mampu mengaplikasikan komputer dalam melakukan simulasi terkait proses random No Pokok Bahasan Subpokok bahasan Metoda Pengajaran Bahan Pustaka Introduction to Probability and Statistics Essential of probability and statistics in telecom Definition some basics quantities Model of probabilities, Axioms, 2, 2 Introduction to discrete random variables Conditional probabilities Probabilities involving random variables Discrete random variables

2 Discrete random variables - 4 Introduction to continuous random variables Multiple random variables Expectation Probability generating functions The binomial random variable The weak law of large numbers Conditional probability Conditional expectation Densities and probabilities Expectation of a single random variable Transform methods,2, 5 Pairs of Random Variables Joint Cumulative Distribution Functions Joint Probability Density Functions Joint Probability Mass Functions Conditional Distribution, Density, and Mass Functions Expected Values Involving Pairs of RV Independent RV Jointly Gaussian RV Transformations of Pairs of RV 6 Multiple Random Variables Joint and Conditional PMFs, CDFs, and PDFs Expectations Involving Multiple Random Variables Gaussian Random Variables in Multiple Dimensions,2,2

3 7 Multiple Random Variables 2 Transformations Involving Multiple Random Variables Estimation and Detection Engineering Application: Linear Prediction of Speech 8 Ujian Tengah Semester 9 Random Processes Definition and Classification Mathematical Tools Stationary and Ergodic Random Processes Properties of the Autocorrelation Function 0 Random Processes 2 Gaussian Random Processes Poisson Processes Markov Processes Definition and Examples of Markov Processes Calculating Transition and State Probabilities in Markov Chains Characterization of Markov Chains 2 Markov Processes 2 Continuous Time Markov Processes Engineering Application: A Computer Communication Network Power Spectral Density Definition of PSD The Wiener Khintchine Einstein Theorem,,,

4 4 Random Processes in Linear Systems Bandwidth of a Random Process Spectral Estimation Thermal Noise Engineering Application: PSDs of Digital Modulation Formats Continuous Time Linear Systems Discrete-Time Linear Systems Signal-to-Noise Ratios Engineering Application: An Analog Communication System 5 Simulation Techniques Computer Generation of Random Variables Generation of Random Processes Simulation of Rare Events Simulation of a Coded Digital Communication System 6 Ujian Akhir Semester References: [] John A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, [2] Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye, Essentials of Probability & Statistics for Engineers & Scientists, Pearson, 20

5 [] Scott L.Miller, Donald Childers, Probability and Random Processes, With Applications to Signal Processing, Edition 2, Academic Press, 202 [4] Andy Field, Discovering Statistics Using SPSS (Introducing Statistical Method), rd edition-sage Publications Ltd, Terbitan : Agustus 202 Revisi: Disetujui/Disahkan Oleh : Ketua Program Studi Magister Teknik Elektro Dibuat oleh : Koordinator Mata Kuliah Dr.-Ing. Mudrik Alaydrus Dr.-Ing. Mudrik Alaydrus