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greattom365木蟲 (著名寫手)
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| 摘 要:隨機變量獨立性在概率論中占據(jù)著十分重要的地位,是《概率論與數(shù)理統(tǒng)計》教材中的一個重點,也是學(xué)生學(xué)習(xí)的一個難點,因而其相關(guān)研究一直以來都被作為一個獨立的課題來進行。隨機變量分為離散型隨機變量和連續(xù)型隨機變量,由于在數(shù)學(xué)研究中最常見的是連續(xù)型隨機變量,所以我們在研究時側(cè)重于連續(xù)性隨機變量的獨立性研究。本文總結(jié)了幾種隨機變量獨立性的辨別方法,并給出了一個非常好用的判別隨機變量獨立性的充要條件。并對其進行了詳細的證明推導(dǎo)。文中列舉了幾道具有針對性的例題來熟悉各種辨別法的應(yīng)用情況以及注意事項。 |

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Abstract: The independence of random variables in probability theory occupies a very important position. It is the key to the "Probability and Statistics" textbook , but also a difficulty of students, thus the related research has been being used as an independent subject . Random variables into discrete random variables and continuous random variables, and we study focused on the independence of continuous random variables as the most common in the mathematical study is the continuous random variable. This paper summarizes the identification of several independent random variables, and gives a very nice random variables determine the necessary and sufficient conditions for independence. And a detailed proof of its derivation. The paper cited a few more examples to become familiar with the targeted application of various identification methods and precautions. Keywords: Precautions Independence Probability theory Continuity Targeted |

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