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扑扑扑 · 2020年07月25日

问一道题:NO.PZ2015120604000173

问题如下:

Which of the following statements about the continuous uniform distribution and the normal distribution is most accurate?

选项:

A.

If X~N(μ,σ), then X/σ~N(0,1)

B.

The cumulative distribution function of the continuous uniform distribution is a curve.

C.

If X is a random variable which is continuously uniform distributed, then P(X=a)=0 (a is a specific value).

解释:

C is correct.

If X~N(μ,σ), then (X-μ)/σ~N(0,1), so A is wrong.

The cumulative distribution function of the continuous uniform distribution is a fully straight line ,so B is wrong.

B选项,continuous uniform distribution密度函数图像是一条直线,但累积概率的图像究竟是什么样子呢?为什么还是一条直线?

1 个答案
已采纳答案

星星_品职助教 · 2020年07月26日

同学你好,

如果写出continuous uniform distribution的累积概率函数F(X),会发现是一个分段函数的形式,分成三段,中间那段的图像是一个以1/(b-a)为斜率的直线,而两端那两端都是常数,图像也就还是直线,所以说F(X)是“curve/曲线”是不对的。