统计学,英文,A random variable X is given such that X ∼ N(82

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统计学,英文,
A random variable X is given such that X ∼ N(82,126).
a.One of the different values of X is chosen at random.If this value can be
rounded to the nearest whole number,what is the probability that this whole
number is 84?
b.If we take five independent values of the variable X,find the probability that
not more than one of them is greater than 87.
c.If P(87< X < k) = 0.3,find the value of k.

1.求的是P(84<x<85),首先你要知道cumulative distribution function怎么算,P(84<x<85)=F(85)-F(84)

把μ=82和σ^2=126代入,有

上面和下面分别是解析解和数值解

2.第二题问的是五个独立变量X,至多一个大于87的概率
P(X>87)=0.328

由二项式展开,要么五个都小于87,要么其中一个大于87,而这一个是任意的,1C5选择共有五种,于是概率为
(1-0.328)^5+5*(1-0.328)^4*0.328=0.471482

3.首先可以求解析解,数值解得Erf[5/(6Sqrt(7))]=0.343995,代入得Erf[(k-82)/(6*Sqrt(7))]=0.943995.再数值求解由k=103.451

根据我的经验,国外这种题一般给数值解就可以了.Erf函数一般是要借助计算器或者查表的,考试会用计算器即可,如果你是查表求解的话是\x08给的都是ϕ函数的,要从F函数换算过去.

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