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kentQ · 2025年02月07日

E[X12] = 1786.63 and V[X1] = 1534.36 请问如何算的 谢谢

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NO.PZ2024120401000007

问题如下：

Suppose that the annual profit of two firms, one an incumbent (Big Firm, X1) and the other a startup (Small Firm, X2), can be described with the following probability matrix:

Using the probability matrix for Big Firm and Small Firm, what is the correlation between the profits of these two firms?

选项：

A.

0.384

B.

0.350

C.

23.37

D.

43.7

解释：

The marginal distributions are computed by summing across rows for Big Firm and down columns for Small Firm. They are:

The variance can be computed using E[Xj2]- (E[Xj])2 .

For Big Firm, these values are E[X1] = 6.77% * (-50) + 43.02% * (0) + 34.38% * (10) + 15.83% * (100) = $15.88M, E[X12] = 1786.63 and V[X1] = 1534.36.

For Small Firm, these values are E[X2] = 6.70% * (-1) + 43.19% * (0) + 34.18% * (2) + 15.93% * (4) = $1.25M, E[X22] = 3.98 and V[X2] = 2.41.

The expected value of the cross product is E[X1X2] = ΣΣx1x2Pr(X1 = x1, X2 = x2) = 43.22.

The covariance is E[X1X2]- E [X1]×E[X2] = 43.22- 15.88 * 1.25 = 23.37 and the correlation is 23.37 / sqrt(2.41 * 1534.36) = 0.384.

E[X12] = 1786.63 and V[X1] = 1534.36 请问如何算的 谢谢

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NO.PZ2024120401000007 问题如下 Suppose ththe annuprofit of two firms, one incumbent (Big Firm, X1) anthe other a startup (Small Firm, X2), cscribewith the following probability matrix:Using the probability matrix for Big Firm anSmall Firm, whis the correlation between the profits of these two firms? A.0.384 B.0.350 C.23.37 43.7 The marginstributions are computesumming across rows for Big Firm anwn columns for Small Firm. They are:The varianccomputeusing E[Xj2]- (E[Xj])2 .For Big Firm, these values are E[X1] = 6.77% * (-50) + 43.02% * (0) + 34.38% * (10) + 15.83% * (100) = $15.88M, E[X12] = 1786.63 anV[X1] = 1534.36.For Small Firm, these values are E[X2] = 6.70% * (-1) + 43.19% * (0) + 34.18% * (2) + 15.93% * (4) = $1.25M, E[X22] = 3.98 anV[X2] = 2.41.The expectevalue of the cross prois E[X1X2] = ΣΣx1x2Pr(X1 = x1, X2 = x2) = 43.22.The covarianis E[X1X2]- E [X1]×E[X2] = 43.22- 15.88 * 1.25 = 23.37 anthe correlation is 23.37 / sqrt(2.41 * 1534.36) = 0.384. 不明白\"correlation\" 問的是什麼，然後引伸至解題的步驟另外，不明白的步驟，尤其是 The expectevalue of the cross prois E[X1X2] = ΣΣx1x2Pr(X1 = x1, X2 = x2) = 43.22.The covarianis E[X1X2]- E [X1]×E[X2] = 43.22- 15.88 * 1.25 = 23.37 anthe correlation is 23.37 / sqrt(2.41 * 1534.36) = 0.384.

2025-02-02 21:57 1 · 回答