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SkipperLin · 2020年02月08日

问一道题：NO.PZ2020010303000009

  1. FRM I
  2. Quantitative

问题如下：

Either using a Z table or the Excel function NORM.S.DIST, compute

a. Pr(-1.5 < Z < 0), where Z ∼ N(0, 1)

b. Pr(Z < -1.5), where Z ∼ N(0, 1)

c. Pr(-1.5 < X < 0), where X ∼ N(1, 2)

d. Pr(X > 2), where X ∼ N(1, 2)

e. Pr(W > 12), where W ∼ N(3, 9)

选项：

解释：

a. 43.3%. In Excel, the command to compute this value is NORM.S.DIST(0,TRUE) – NORM.S.DIST(-1.5,TRUE).

b. 6.7%. In Excel, the command to compute this value is NORM.S.DIST(-1.5,TRUE).

c. 20.1%. In Excel, the command to compute this value is NORM.S.DIST((0 – 1)/SQRT(2),TRUE) – NORM.S.DIST((-1.5-1)>SQRT(2),TRUE).

d. 24.0%. In Excel, the command to compute this value is 1 – NORM.S.DIST((2 – 1)/SQRT(2),TRUE).

e. 0.13%. In Excel, the command to compute this value is 1 – NORM.S.DIST((12 – 3)/3,TRUE).

请问第三题这种应该怎么转换

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1 个答案

品职答疑小助手雍 · 2020年02月08日

同学你好，第三问的分布是服从（1,2）的正态分布，所以0 到均值1的距离就是（0-1）/根号2 倍的标准差（后面公式的前半部分就是求负无穷到这个点的累计概率），-1.5到均值1的距离就是（-1.5-1）/根号2 倍的标准差（后面公式的后半部分就是求负无穷到这个点的累计概率）。

负无穷到0的累计概率减去负无穷到-1.5的累计概率，就是得到他俩之间的累计概率了。

SkipperLin · 2020年02月09日

了解 请问如果是查表的话 是不是先看表算出Pr(-1.5 < X < 0)在标准正态分布的概率 然后假设这个概率是x，得到x之后我们在x*sqrt(2) + 1也可以？

品职答疑小助手雍 · 2020年02月09日

不行，不能用概率*根号2这样。这期间的概率分布不是对于标准正态和（1,2）的正态不是等比例的。

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