简答题: 设随机变量X1，X2，X3相互独立，其中X1与X2均服从标准正态分布，X3的概率分布为P{X3=0}=P{X3=1}=<img width="24" height="62" src="http://www.weimei168.com/uploads/202208/20210427232717_1475.gif" />，Y=X3X1+(1-X3)X2． (Ⅰ)求二维随机变量(X1，Y)的分布函数，结果用标准正态分布函数<img width="26" height="24" src="http://www.weimei168.com/uploads/202208/20210427232719_2569.gif" />(x)表示； (Ⅱ)证明随机变量Y服从标准正态分布．

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当x→0+时，下列无穷小量中是最高阶的是( )．

A <img width="117" height="41" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232647_7101.jpg" /> B <img width="143" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232648_8351.jpg" /> C <img width="99" height="44" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232649_8721.jpg" /> D <img width="143" height="44" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232650_9601.jpg" />

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设函数f(x)在区间(-1，1)内有定义，且，则( )

A <img width="385" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232653_1163.jpg" /> B <img width="361" height="43" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232654_1632.jpg" /> C <img width="394" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232655_2569.jpg" /> D <img width="361" height="43" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232656_3819.jpg" />

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设函数f(x，y)在点(0，0)处可微f(0，0)=0，且非零向量d与n垂直，则( )．

A <img width="358" height="51" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232658_5070.jpg" /> B <img width="363" height="51" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232659_6944.jpg" /> C <img width="357" height="52" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232700_6320.jpg" /> D <img width="362" height="52" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232702_1789.jpg" />

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设R为幂级数的收敛半径，r是实数，则( )．

A <img width="258" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232704_3038.jpg" /> B <img width="258" height="48" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232704_9288.jpg" /> C <img width="263" height="48" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232706_4132.jpg" /> D <img width="263" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232707_0684.jpg" />

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若矩阵A经初等列变换化成B，则( )．

A 存在矩阵P，使得PA=B B 存在矩阵P，使得BP=A C 存在矩阵P，使得PB=A D 方程组Ax=0与Bx=0同解

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已知直线相交于一点，法向量，则( )．

A <img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />可由<img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />，<img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />线性表示 B <img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />可由<img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />，<img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />线性表示 C <img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />可由<img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />，<img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />线性表示 D <img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />，<img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />，<img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />线性无关

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设A，B，C为三个随机事件，P(A)=P(B)=P(C)=，P(AB)=O,P(AC)=P(BC)=1，则A，B，C中恰有一个事件发生的概率为( )．

A <img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232714_9844.gif" /> B <img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232715_6319.gif" /> C <img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232717_1475.gif" /> D <img width="32" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232717_9795.gif" />

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设X1，X2，…，Xn为来自总体X的简单随机样本，其中P{X=0}=P{X=1}=，(x) 表示标准正态分布函数，则利用中心极限定理可得的近似值为( )．

A 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1) B <img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1) C 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(0．2) D <img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(0．2)

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