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"The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. The goal of this book is to bring together the bulk of these results, presenting the theory in a unified way, explaining relations and implications of the results. It will present basic definitions and characterizations, followed by a collection of relevant inequalities. These are then applied to characterize almost sure and weak convergence of sequences of associated variables. It will also cover applications of positive dependence to the characterization of asymptotic results in nonparametric statistics. "

"ABSTRAK Integral Henstock-Kurzweil merupakan hasil dari perkembangan integral Riemann. Dalam tulisan ini akan ditunjukkan bagaimana sifat-sifat integral Riemann dan Integral Henstock-Kurzweil dari fungsi bernilai di ruang Banach. Selain itu, akan ditunjukkan perbandingan antara integral Riemann dan integral Henstock-Kurzweil untuk fungsi bernilai di ruang Banach berdimensi takhingga.

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ABSTRAK Henstock-Kurzweil integrable is Generalized Riemann integrable. In this paper, will show the property of Riemann integrable and Henstockk-Kurzweil integrable of function Banach-valued. And comparison Riemann integrable and Henstock- Kurzweil integrable for infinite Banach space."

"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."