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浙江大學 概率論

浙江大學 概率論

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內容介紹

    簡介:概率論是研究和揭示自然界和人類社會隨機現象規律的一門學科,是統計理論和方法的基礎,與數學 的其他分支有著密切聯系,并在各個領域有著廣泛的應用。本課程主要闡述概率論的基本思想,介紹研究隨 機現象的基本方法以及基本結果

    預修要求:已修過數學分析和線性代數

    課程主要內容:

    (一)隨機事件及其概率
    1. 隨機現象與統計規律性
    2. 概率的古典定義
    3. 概率的公理化定義
    4. 條件概率與事件的獨立性
    (二)隨機變量和分布函數
    1. 離散型隨機變量及其分布
    2. 分布函數與連續型隨機變量
    3. 隨機向量
    4. 條件分布、隨機變量的獨立性
    5. 隨機變量的函數及其分布
    (三)數字特征
    1. 數學期望
    2. 方差、矩與相關系數
    3. 特征函數
    4. 多元正態分布
    (四)極限定理
    1. 依分布收斂與中心極限定理
    2. 依概率收斂與弱大數定律
    3. 以概率1收斂與強大數定律

    選用教材或參考書:

    教材: 《概率論》,林正炎、蘇中根編,浙江大學出版社,2003(第二版)。  
    主要參考書: 《概率論基礎》(第二版),李賢平編,高等教育出版社。 

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