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"Suatu pengujian dibutuhkan untuk membandingkan mean dari dua populasi. Pada pengujian beda dua mean populasi ketika kedua variansi populasi tidak diketahui dan diasumsikan variansi sama, statistik ujinya dicari dengan menggunakan dalil limit pusat ketika ukuran sampel besar. Sedangkan ketika ukuran sampel kecil, digunakan uji likelihood rasio. Jika diasumsikan variansi populasi tidak sama, maka statistik ujinya didapat dari penurunan terhadap statistik Welch. Pada pengujian beda dua mean populasi ketika salah satu variansi populasi tidak diketahui, digunakan metode Satterthwaite untuk mencari aproksimasi dari derajat bebasnya. Penaksir dari derajat bebas yang diperoleh merupakan penaksir yang bias. Oleh karena itu, dicari penaksir dari derajat bebas yang tak bias dan memiliki variansi lebih kecil dari penaksir derajat bebas yang bias. Pada tugas akhir ini dibahas contoh pengujian untuk ketiga pengujian tersebut.

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A test is required to compare the mean of two population. On the test of the difference between two population means when both of the population variances are unknown and with the assumption of the same variance, the test statistic is found using the central limit theorem in which the sample size is large. When the sample size is small, the likelihood ratio test is used. If both of the population variances aren’t assumed to be equal, then the test statistic is obtained from the derivation of the Welch’s statistic.

On the test of the difference between two population means when one of the population variance is unknown, the Satterthwaite’s method is used to find the approximation of the degrees of freedom. The estimator of the degrees of freedom obtained is biased. Therefore, the unbiased estimator of degrees of freedom will be determined and it has smaller variance than the biased estimator of the degrees of freedom. This minithesis discussed about the example of the test for those three tests."

"This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used, the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics. "

"The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior)."

"Population processes are stochastic models for systems involving a number of similar particles. Examples include models for chemical reactions and for epidemics. The model may involve a finite number of attributes, or even a continuum. This monograph considers approximations that are possible when the number of particles is large. The models considered will involve a finite number of different types of particles."

"Tesis ini membahas faktor-faktor yang memengaruhi keputusan perusahaan yang berada di bawah threshold Pajak Pertambahan Nilai PPN dalam melakukan voluntary registration menjadi Pengusaha Kena Pajak PKP dan dampak status PKP tersebut terhadap gross profit dan value added perusahaan. Berdasarkan kerangka konseptual dan dengan menggunakan data periode 2011-2016, hasil estimasi empiris mendukung hipotesis bahwa rasio penjualan business-to-consumer B2C yang semakin rendah, rasio biaya input dan kompetitivitas industri yang semakin tinggi akan meningkatkan probabilita perusahaan melakukan voluntary regisration PPN. Selain itu, gross profit dan value added perusahaan juga dapat meningkat dengan perusahaan menjadi PKP.

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This thesis discusses the factors that influence the firm decision which is under threshold of Value Added Tax VAT system in conducting voluntary registration to Taxable Entrepreneur for VAT Purposes PKP and the impact of their PKP status to their gross profit and value added. Based on the conceptual framework and using the 2011 2016 period data, the empirical estimation results support the hypothesis that the lower the business to consumer B2C sales ratio, the higher input cost ratio and industry competitiveness ratio will increase the probability of the firm 39 s voluntary registration of VAT. In addition, firm rsquo s gross profit and value added can also increase if its status is PKP."

"Dalam penelitian ini telah dilakukan sintesis homopolimer poli(etil akrilat) dengan metode Atom Transfer Radical Polymerization (ATRP) untuk mengetahui pengaruh waktu dan suhu reaksi, serta konsentrasi ligan, katalis, inisiator, dan monomer terhadap %konversi, temperatur transisi gelas (Tg), dan distribusi berat molekul. Dari hasil penelitian didapatkan bahwa semakin tinggi waktu dan suhu reaksi, maka %konversi semakin tinggi. Komposisi variasi yang optimum terhadap %konversi adalah 100:1:0,5:1 (Monomer:Ligan:Katalis:Inisiator) dengan waktu reaksi 6 jam pada suhu 110˚C, mencapai 78%. Semakin tinggi konsentrasi ligan, maka indeks polidispersitas semakin kecil. Semakin tinggi konsentrasi katalis, maka indeks polidispersitas semakin besar. Terbentuknya poli(etil akrilat) ditunjukkan oleh hasil karakterisasi dengan Fourier Transform Infra Red (FTIR) dengan hilangnya puncak C=C, Gel Permeation Chromatography (GPC) yang memiliki indeks polidispersitas optimum sebesar 2,50 (100:1:0,5:1) dengan berat rata-rata berat molekul (Mw) 7.085, dan Differential Scanning Calorimetry (DSC) dengan munculnya puncak temperatur transisi gelas (Tg) pada suhu -58,15˚C. Dengan demikian poli(etil akrilat) telah berhasil disintesis.

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In this research, the synthesis of homopolymer poly(ethyl acrylate) by the method of Atom Transfer Radical Polymerization (ATRP) has been done to study the effect of the time and temperature of reaction, and concentration of ligands, catalysts, inisiators, and monomers for %conversion, glass transition temperature (Tg), and molecular weight distribution. The result showed that the higher time and temperature of reaction were, the higher of the %conversion. The optimum composition variations of the %conversion is 100:1:0,5:1 (Monomer:Ligand:Catalyst:Initiator) with time of reaction 6 hour at 110˚C reaches 78%. The higher of the ligand concentration, then the smaller of the polydispersity index. The higher of the catalyst concentration, the greater of the polydispersity index. The formation of poly(ethyl acrylate) shown by the results of characterization by Fourier Transform Infra Red (FTIR) with the lost of the C=C peak, Gel Permeation Chromatography (GPC) which has optimum polydipersity index 2,50 (100:1:0,5:1) with weight average molecular weight (Mw) 7.085, and Differential Scanning Calorimetry (DSC) with the appearance of the peak glass transition temperature (Tg) at -58,15˚C. Therefore, poly(ethyl acrylate) has successfully been synthesized."

"ABSTRACTSkripsi ini membahas model predator-prey dengan Allee effect pada populasi prey dan pemanenan pada kedua populasi. Allee effect adalah situasi ketika pertumbuhan populasi pada populasi berkepadatan rendah berkurang ketika ukuran populasi nya berada dibawah koefisien Allee. Intervensi pemanenan ilegal pada populasi predator dan prey diperhitungkan ke dalam model bersama dengan persaingan internal pada populasi predator. Analisis matematika digunakan untuk menemukan titik ekuilibrium. Stabilitas lokal untuk titik-titik ekuilibrium kepunahan dan koeksistensi dianalisis menggunakan metode linearisasi dengan matriks Jacobian. Analisa bidang fase juga diberikan untuk memberikan interpretasi yang lebih baik untuk hasil sebelumnya. Beberapa simulasi numerik diberikan untuk menunjukkan bagaimana intervensi pemanenan dapat menyebabkan kepunahan pada kedua populasi ketika tidak terkontrol.

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ABSTRACTThis thesis discussed predator prey model with Allee effect on prey population and harvesting in both populations. Allee effect is a situation for a small population when the population growth is reduced when it is under overcrowding. Intervention of illegal harvesting in both predator and prey population included into the model along with internal competition of predator population. Mathematical analysis to find the equilibrium points conducted analytically. Local stability for the extinction and coexistence equilibrium points are analyze using the linearization method with the Jacobian matrix. Phase portrait analysis also given to give a better interpretation for the previous result. Some numerical simulation are given to show how harvesting intervention can lead into an extinction of both population when it is uncontrolled. This thesis discussed predator prey model with Allee effect on prey population and harvesting in both populations. Allee effect is a situation for a small population when the population growth is reduced when it is under overcrowding. Intervention of illegal harvesting in both predator and prey population included into the model along with internal competition of predator population. Mathematical analysis to find the equilibrium points conducted analytically. Local stability for the extinction and coexistence equilibrium points are analyze using the linearization method with the Jacobian matrix. Phase portrait analysis also given to give a better interpretation for the previous result. Some numerical simulation are given to show how harvesting intervention can lead into an extinction of both population when it is uncontrolled."

"Pekerja commuter yang berasal dari Depok menuju daerah Sudirman mayoritas memilih KRL sebagai moda transportasi. Saat ini pemerintah berencana untuk megoperasikan feeder bus dari Depok menuju Ragunan dan selanjutnya menggunakan bus transjakarta koridor 6. Untuk mengetahui probabilitas orang yang memilih bus digunakan analisa dari model logit. Responden pengguna KRL asal Sukmajaya mempunyai probabilitas memilih bus yang lebih besar dibandingkan dengan responden pengguna KRL dari berbagai Kecamatan. Dari hasil analisa uji sensitivitas diketahui bahwa atribut yang paling sensitif mempengaruhi probabilitas pemilihan moda adalah biaya dan waktu. Dengan adanya perubahan nilai atribut biaya dan waktu secara gradual, nilai probabilitas memilih bus sebesar 0,5 akan tercapai jika terdapat kondisi sebagai berikut: biaya bus feeder Rp.0 untuk responden dari berbagai Kecamatan, biaya bus feeder Rp.1700,00 untuk responden dari Sukmajaya, waktu bus feeder 10 menit untuk dari berbagai Kecamatan, dan waktu bus feeder 28 menit untuk responden dari Sukmajaya.

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Commuter workers who come from Depok to Sudirman area majority choose KRL as a mode of transportation. Currently, the government plans to operate feeder bus from Depok to Ragunan and then use the bus corridor Transjakarta 6. To determine the probability of people choosing the bus is used the analysis of the logit model. Respondents of KRL user from Sukmajaya have a probability of choosing bus bigger than respondents KRL user of the various Districts.

From the analysis, test sensitivity is known that the most sensitive attributes affect the probability of modal choice are cost and time. If there are changes in cost and time attribute values gradually, the probability of choosing bus of 0.5 would be achieved if the following conditions exist: the cost of feeder bus is Rp.0 for respondents from the various Districts, the cost of feeder bus is Rp.1700, 00 for respondents from Sukmajaya, the time of feeder bus is 10 minutes for respondents from the various Districts, and the time of feeder bus is 28 minutes for respondents from Sukmajaya."