KETERKAITAN ANTARA KONVERGEN ALMOST SURELY, KONVERGEN DALAM PROBABILITAS, KONVERGEN DALAM MEAN, DAN KONVERGEN DALAM DISTRIBUSI

Vira Agusta, Nurweni Putri, Maya Sari Syahrul

Abstract


Pada penelitian ini mengkaji keterkaitan antara konvergen almost surely, konvergen dalam probabilitas, konvergen dalam mean, dan konvergen dalam distribusi. Jika barisan variabel random  konvergen almost surely ke suatu variabel random X, maka konvergen dalam probabilitas ke variabel random ke X. Jika barisan variabel random  konvergen dalam probabilitas ke variabel random X maka konvergen dalam mean ke  X. Jika barisan variabel random  konvergen dalam probabilitas ke variabel random X maka konvergen dalam distribusi ke X.

Abstract

In this research the relations between convergence almost surely, convergence in probability, convergence in mean, and convergence in distribution. If the sequence of random variables  converges almost surely to a random variable X, then it converges in probability to the random variable to X. If the sequence of random variables  converges in probability to a random variable X, then it converges in mean to the random variable to X. If the sequence of random variables  converges in probability to a random variable X, then it converges in the distribution to the random variable to X.


Keywords


ruang probabilitas, konvergen almost surely, konvergen dalam probabilitas, konvergen dalam mean, konvergen dalam distribusi

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DOI: https://doi.org/10.15548/map.v1i2.1177
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References


Ash, R.N. 1972. Real Analysis and Probability, Academic Press inc, London.

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Casella, G. dan R. L. Berger. 1990. Statistical Inference. Ed. Ke-1 Wadsworth & Brooks/Cole, Pasific Grove, California.

Subanar. 2013. Statistika Matematika, Probabilitas, Distribusi, dan Asimtotis dalam Statistika. Graha Ilmu, Yogyakarta.

Subanar. 2013. Statistika Matematika. Graha Ilmu, Yogyakarta.


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