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🌅 🌅多吉旺珍🌞🌞 · 2020年07月28日

问一道题:NO.PZ2018062016000082 [ CFA I ]

问题如下:

The stock of AAA company has a 30% probability to rise every year, if every annual trial is independent from each other, the probability that the stock will rise more than 1 time in the next 3 years is:

选项:

A.

0.145

B.

0.216

C.

0.377

解释:

B is correct. Based on the corresponding formula:

p(x)=P(X=x)=(nx)px(1p)nxp{(x)}=P{(X=x)}={(\begin{array}{c}n\\x\end{array})}p^x{(1-p)}^{n-x}, n = 3 and p = 0.30.

p(2)=3!(32)!2!×0.32(10.3)1=(3)(0.09)(0.7)=0.189p(2)=\frac{3!}{(3-2)!2!}\times0.3^2(1-0.3)^1=\left(3\right)\left(0.09\right)\left(0.7\right)=0.189.

p(3)=3!(33)!3!×0.33(10.3)0=(1)(0.027)(1)=0.027p(3)=\frac{3!}{(3-3)!3!}\times0.3^3(1-0.3)^0=\left(1\right)\left(0.027\right)\left(1\right)=0.027\cdot

The required probability is: p(2) + p(3) = 0.189 + 0.027 = 0.216

老师您好 这道题的解题思路和所运用知识点您能帮忙解决一下吗
1 个答案

星星_品职助教 · 2020年07月28日

同学你好,

这道题是二项分布的考点。股票的变化只有两种可能,上涨或下跌,所以是个伯努利变量。做多次伯努利试验所产生的的成功“次数”的分布就是二项分布。

这道题问在三次试验中,股票上涨超过1次的概率。所以就是要么2次上涨,要么3次全上涨。就是P(x=2) + P(x=3),直接代入二项分布的公式解题即可

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NO.PZ2018062016000082 问题如下 The stoof Acompany ha 30% probability to rise every year, if every annutriis inpennt from eaother, the probability ththe stowill rise more th1 time in the next 3 years is: A.0.145 B.0.216 C.0.377 B is correct. Baseon the corresponng formula:p(x)=P(X=x)=(nx)px(1−p)n−xp{(x)}=P{(X=x)}={(\begin{array}{c}n\\x\enarray})}p^x{(1-p)}^{n-x}p(x)=P(X=x)=(nx​)px(1−p)n−x, n = 3 anp = 0.30.p(2)=3!(3−2)!2!×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189p(2)=\frac{3!}{(3-2)!2!}\times0.3^2(1-0.3)^1=\left(3\right)\left(0.09\right)\left(0.7\right)=0.189p(2)=(3−2)!2!3!​×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189.p(3)=3!(3−3)!3!×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅p(3)=\frac{3!}{(3-3)!3!}\times0.3^3(1-0.3)^0=\left(1\right)\left(0.027\right)\left(1\right)=0.027\ctp(3)=(3−3)!3!3!​×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅The requireprobability is: p(2) + p(3) = 0.189 + 0.027 = 0.216 我算的是接下来3年均大于, 也就是p1+p2+p3均大于的情况, 请问这样理解为什么不对

2023-11-05 19:38 2 · 回答

NO.PZ2018062016000082 问题如下 The stoof Acompany ha 30% probability to rise every year, if every annutriis inpennt from eaother, the probability ththe stowill rise more th1 time in the next 3 years is: A.0.145 B.0.216 C.0.377 B is correct. Baseon the corresponng formula:p(x)=P(X=x)=(nx)px(1−p)n−xp{(x)}=P{(X=x)}={(\begin{array}{c}n\\x\enarray})}p^x{(1-p)}^{n-x}p(x)=P(X=x)=(nx​)px(1−p)n−x, n = 3 anp = 0.30.p(2)=3!(3−2)!2!×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189p(2)=\frac{3!}{(3-2)!2!}\times0.3^2(1-0.3)^1=\left(3\right)\left(0.09\right)\left(0.7\right)=0.189p(2)=(3−2)!2!3!​×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189.p(3)=3!(3−3)!3!×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅p(3)=\frac{3!}{(3-3)!3!}\times0.3^3(1-0.3)^0=\left(1\right)\left(0.027\right)\left(1\right)=0.027\ctp(3)=(3−3)!3!3!​×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅The requireprobability is: p(2) + p(3) = 0.189 + 0.027 = 0.216 谢谢解答

2022-11-04 18:24 1 · 回答

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2022-08-21 16:46 1 · 回答

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2021-09-20 17:41 1 · 回答