The Mathematics of Value-at-Risk
As was mentioned on page 3, the expected value of a linear combination of random variables is the linear combination of the expected values. Suppose we have random variables X1,X2,…,Xn, and coefficients α1, α2,…, αn. Then it follows that. E[α1X1 + α2X2 +…+ αnXn] = α1E[X1] + α2E[X2] +…+ E[αnXn]. ................
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