对于任意随机变量<img style="backface-visibility: hidden; background-color: transparent; border-bottom-color: rgb(51, 51, 51); border-bottom-style: none; border-bottom-width: 0px; border-image-outset: 0; border-image-repeat: stretch; border-image-slice: 100%; border-image-source: none; border-image-width: 1; border-left-color: rgb(51, 51, 51); border-left-style: none; border-left-width: 0px; border-right-color: rgb(51, 51, 51); border-right-style: none; b
A.<img style="backface-visibility: hidden; background-color: transparent; border-bottom-color: rgb(102, 102, 102); border-bottom-style: none; border-bottom-width: 0px; border-image-outset: 0; border-image-repeat: stretch; border-image-slice: 100%; border-image-source: none; border-image-width: 1; border-left-color: rgb(102, 102, 102); border-left-style: none; border-left-width: 0px; border-right-color: rgb(102, 102, 102); border-right-style: none
时间:2024-03-10 16:50:04
相似题目
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设X为随机变量,其方差存在,C为任意非零常数,则下列等式中正确的是()
A . D(X+C)=D(X)
B . D(X+C)=D(X)+C
C . D(X-C)=D(X)-C
D . D(CX)=CD(X)
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如果一个随机变量允许在某个给定的范围内任意取值,则它就是一个()
A . 随机数
B . 随机数分布
C . 离散的随机变量
D . 连续的随机变量
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(5P111)设随机变量X有期望E(X)与方差D(X)则对任意正数£,有()
(5P111)设随机变量X有期望E(X)与方差D(X)则对任意正数£,有()
A.<img src='https://img2.soutiyun.com/ask/uploadfile/3915001-3918000/3a87d554cfc3d2bdca42f77747cedc79.jpg' />
B.<img src='https://img2.soutiyun.com/ask/uploadfile/3915001-3918000/d12249f6930a9365c6685073b935be73.jpg' />
C.<img src='https://img2.soutiyun.com/ask/uploadfile/3915001-3918000/3c88ea9ebc5c86e226bbc8d05fc3c652.jpg' />
D.<img src='https://img2.soutiyun.com/ask/uploadfile/3915001-3918000/b81b384d49872f55f529158eca40c3a1.jpg' />
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对于任意一个二维随机变量,由它的两个边缘分布函数可以确定出它的联合分布函数.
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设随机变量(X,Y)的密度函数为<img src='https://img2.soutiyun.com/latex/latex.action' />
则概率P(X<0.5,Y<0.6)为( ).
A.0.5 B.0.3
C.<img src='https://img2.soutiyun.com/latex/latex.action' />
D.0.4
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随机变量X的概率密度<img src='https://img2.soutiyun.com/latex/latex.action' />,则D(X)=( )
A.<img src='https://img2.soutiyun.com/latex/latex.action' />
B.<img src='https://img2.soutiyun.com/latex/latex.action' />
C.<img src='https://img2.soutiyun.com/latex/latex.action' />
D.<img src='https://img2.soutiyun.com/latex/latex.action' />
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设随机变量X的概率密度<img src='https://img2.soutiyun.com/latex/latex.action' />常数c=( ).
A.<img src='https://img2.soutiyun.com/latex/latex.action' />B.<img src='https://img2.soutiyun.com/latex/latex.action' />C.4 D.5
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设连续型随机变量X的概率密度p(x),则当( )时,<img src='https://img2.soutiyun.com/ask/2019-06-21/929983021545511.png' />称其为随机变量X的数学期望
A.<img src='https://img2.soutiyun.com/ask/2019-06-21/929983033254112.png' />收敛 B.p(x)为有界函数
C.<img src='https://img2.soutiyun.com/ask/2019-06-21/92998305557769.png' />D.<img src='https://img2.soutiyun.com/ask/2019-06-21/929983074420875.png' />绝对收敛
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随机变量X的概率密度为<img src='https://img2.soutiyun.com/ask/2020-02-18/950883744337956.png' />,则常数A=( ).
A.3
B.0
C.1
D.2
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设随机变量X的概率密度为<img src='https://img2.soutiyun.com/latex/latex.action' />,则E(X)=( )
A.<img src='https://img2.soutiyun.com/latex/latex.action' />
B.<img src='https://img2.soutiyun.com/latex/latex.action' />
C.<img src='https://img2.soutiyun.com/latex/latex.action' />
D.<img src='https://img2.soutiyun.com/latex/latex.action' />
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设随机变量X的分布函数<img src='https://img2.soutiyun.com/latex/latex.action' />,则E(X)=( )
A.<img src='https://img2.soutiyun.com/latex/latex.action' />
B.<img src='https://img2.soutiyun.com/latex/latex.action' />
C.<img src='https://img2.soutiyun.com/latex/latex.action' />
D.<img src='https://img2.soutiyun.com/latex/latex.action' />
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设随机事件A在第i次独立试验中发生的概率为p<sub>i</sub>,i=1,2,...,n。m表示事件A在n次试验中发生的次数,则对于任意正数ε{ε>0},证明<img src='https://img2.soutiyun.com/ask/2020-12-28/978025287070883.jpg' />
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设有一连续随机变量,其概率密度函数为<img src="https://img2.soutiyun.com/ask/2020-12-17/977093017200649.png"/>试求:
(1)信源X的熵H<sub>C</sub>(X); (2)Y= X+A(A>0)的熵H<sub>C</sub>(Y); (3)Y= 2X的熵H<sub>C</sub>(Y)。
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5、对任意两个随机变量X ,Y ,则必有E(X Y ) = E(X ) E(Y ).
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设X是一随机变量,a为任意实数,EX是X的数学期望,则()。
A.E(X-a)2=E(X-EX)2
B. E(X-a)2≥E(X-EX)2
C. E(X-a)2<E(X-EX)2
D. E(X-a)2=0
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若盒中有5个球,其中2个白球3个黑球,现从中任意取3个球,设随机变量X为取得白球的个数。求:(1)随机变量X的分布;(2)数学期望EX,方差DX。
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3、对于任意一个二维随机变量,由其联合分布函数可以确定出它的两个边缘分布函数.
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6、对于任意两个随机变量X和Y,若D(X+Y)=DX+DY,则()
A.X和Y相互独立
B.X和Y不相互独立
C.D(XY)=DXDY
D.E(XY)=EXEY
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43、对任意两个随机变量X和Y,以下选项正确的是().
A.D (X +Y ) = D (X ) + D (Y )
B.E(X +Y ) = E(X ) + E(Y )
C.E(X Y ) = E(X ) E(Y )
D.D (X Y ) = D (X ) D (Y )
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25、设随机变量(X,Y)的概率密度函数为<img style="border-bottom-color: currentColor; border-bottom-style: none; border-bottom-width: 0px; border-image-outset: 0; border-image-repeat: stretch; border-image-slice: 100%; border-image-source: none; border-image-width: 1; border-left-color: currentColor; border-left-style: none; border-left-width: 0px; border-right-color: currentColor; border-right-style: none; border-right-width: 0px; border-top-color: currentColor;
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设随机变量(X ,Y )的联合分布密度为<img style="backface-visibility: hidden; border-bottom-color: rgb(51, 51, 51); border-bottom-style: none; border-bottom-width: 0px; border-image-outset: 0; border-image-repeat: stretch; border-image-slice: 100%; border-image-source: none; border-image-width: 1; border-left-color: rgb(51, 51, 51); border-left-style: none; border-left-width: 0px; border-right-color: rgb(51, 51, 51); border-right-style: none; border-right-width:
A.<img style="backface-visibility: hidden; background-color: transparent; border-bottom-color: rgb(255, 97, 31); border-bottom-style: none; border-bottom-width: 0px; border-image-outset: 0; border-image-repeat: stretch; border-image-slice: 100%; border-image-source: none; border-image-width: 1; border-left-color: rgb(255, 97, 31); border-left-style: none; border-left-width: 0px; border-right-color: rgb(255, 97, 31); border-right-style: none; bord
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已知随机变量X的期望EX及方差DX,而分布未知,则对于任意实数a,b(a<b),都可以估计出概率的是().
A.P(a<X<b)
B.P(-a<X<a)
C.P(a<X-EX<b)
D.P(X-EX|<a)
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5、对于任意一个二维随机变量,由它的联合分布函数可以确定它的两个边缘分布函数,反过来,由它的两个边缘分布函数也可以确定出它的联合分布函数.
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10、随机变量是用来代表总体的任意数值的,随机变数是随机变量的一组数据,代表总体的随机样本资料,可用来估计总体参数。