Multivariate Random Variables是FRM考試的內容，考生在備考中一定要對相關內容有所掌握。那么，學習FRM考試 Multivariate Random Variables能學到什么？看GARP協會如何說明？

After completing this reading, you should be able to:

? Explain how a probability matrix can be used to express a probability mass function.

? Compute the marginal and conditional distributions of a discrete bivariate random variable.

? Explain how the expectation of a function is computed for a bivariate discrete random variable.

? Define covariance and explain what it measures.

? Explain the relationship between the covariance and correlation of two random variables, and how these are related to the independence of the two variables.

? Explain the effects of applying linear transformations on the covariance and correlation between two random variables.

? Compute the variance of a weighted sum of two random variables.

? Compute the conditional expectation of a component of a bivariate random variable.

? Describe the features of an independent and identically distributed (iid) sequence of random variables.

? Explain how the iid property is helpful in computing the mean and variance of a sum of iid random variables.

完成本閱讀后，您應該能夠：

?解釋如何使用概率矩陣來表示概率質量函數。

?計算離散二元隨機變量的邊際分布和條件分布。

?解釋如何計算二元離散隨機變量的函數期望值。

?定義協方差并解釋其測量的內容。

?解釋兩個隨機變量的協方差和相關性之間的關系，以及它們如何與兩個變量的獨立性相關。

?解釋應用線性變換對兩個隨機變量之間的協方差和相關性的影響。

?計算兩個隨機變量加權和的方差。

?計算二元隨機變量組成部分的條件期望。

?描述獨立同分布（iid）隨機變量序列的特征。

?解釋iid屬性如何有助于計算iid隨機變量總和的均值和方差。

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