联合概率分布:离散与连续随机变量.pdf

联合概率分布:离散与连续随机变量.pdf

  1. 1、本文档共4页,可阅读全部内容。
  2. 2、有哪些信誉好的足球投注网站(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
  3. 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载
  4. 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
联合概率分布:离散与连续随机变量

Math 370/408, Actuarial Problemsolving A.J. Hildebrand Joint Distributions, Discrete Case In the following, X and Y are discrete random variables. 1. Joint distribution (joint p.m.f.): • Definition: f (x, y) = P (X = x, Y = y) • Properties: (1) f (x, y) ≥ 0, (2) f (x, y) = 1 x,y • Representation: The most natural representation of a joint discrete distribution is as a distribution matrix, with rows and columns indexed by x and y , and the xy-entry being f (x, y). This is analogous to the representation of ordinary discrete distributions as a single-row table. As in the one-dimensional case, the entries in a distribution matrix must be nonnegative and add up to 1. 2. Marginal distributions: The distributions of X and Y , when considered separately. • Definition: • fX (x) = P (X = x) = f (x, y) y • fY (y) = P (Y = y) = f (x, y) x • Connection with distribution matrix: The marginal distributions fX (x) and fY (y) can be obtained from the distribution matrix as the row sums and column sums of the entries. These sums can be entered in the “margins” of the matrix as an additional column and row. • Expectation and variance: µX , µY , σ2 , σ2 denote the (ordinary) expectations and X Y variances of X and Y , computed as usual: µX = xfX (x), etc. x 3. Computations with joint distributions: • Probabilities: Pr

文档评论(0)

yan698698 + 关注
实名认证
内容提供者

该用户很懒,什么也没介绍

1亿VIP精品文档

相关文档