设p＞1，证明不等式<img src='https://img2.soutiyun.com/ask/2021-01-18/979838709003026.png' />

设z是任一复数,证明<img src='https://img2.soutiyun.com/ask/2021-01-13/9794048514659.png' />

求下列等式：设<img src='https://img2.soutiyun.com/ask/2020-11-11/973957900743664.png' />

设A非奇异，λ_i是方阵A^TA的特征值，证明：<img src='https://img2.soutiyun.com/ask/2020-11-27/975337614484347.jpg' />

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

设<img src='https://img2.soutiyun.com/latex/latex.action' />，则点x=1是f(x)的( )。

设<img src='https://img2.soutiyun.com/latex/latex.action' />(n=1，2…)，则E(X)=( )．

设函数g(x)=1+x，且当x≠0时，<img src='https://img2.soutiyun.com/ask/2020-02-18/950885721858992.png' />，则<img src='https://img2.soutiyun.com/ask/2020-02-18/950885746436467.png' />等于( )

设G₁,G₂是两个群，证明:<img src='https://img2.soutiyun.com/ask/2020-08-12/966069714066236.png' />

设<img src='https://img2.soutiyun.com/ask/2020-12-15/976910006079741.png' />为同一区间上的可导函数,证明

设随机事件A在第i次独立试验中发生的概率为p_i，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' />

设P(A)=a，P(B)=b，P(A+B)=c，则<img src='https://img2.soutiyun.com/latex/latex.action' />为( )

设A、B为任意两事件，且<img src='https://img2.soutiyun.com/ask/2020-03-06/952348543191874.png' />，P(B)＞0，则下列选项必然成立的是( )

设a≠0,|r|＜1,求<img src='https://img2.soutiyun.com/ask/2020-10-26/972583970755153.png' />

设图中回路各阀的调整压力为p₁>p₂>p₃，那么回路能实现（）调压。<img src='https://img2.soutiyun.com/shangxueba/ask/18354001-18357000/18356310/2015062410015243718.jpg' />

证明不等式:<img src='https://img2.soutiyun.com/shangxueba/ask/51399001-51402000/51401966/977847325438542.png' />.

设f(x)为连续函数,且满足等式<img src='https://img2.soutiyun.com/shangxueba/ask/51381001-51384000/51383367/97672305236883.png' />则<img src='https://img2.soutiyun.com/shangxueba/ask/51381001-51384000/51383367/976723063701479.png' />=().

证明定理3:15中的等式<img src='https://img2.soutiyun.com/ask/2021-01-02/978463581870021.png' />

设随机变量（X，Y）的分布律为&nbsp;&nbsp;&nbsp;<img src="https://img2.soutiyun.com/shangxueba/ask/19434001-19437000/19435034/c33cb56-chaoxing2016-268566.png"/>则P{X=2｜Y=2}=（）

设α₁，α₂，···，α_m和β₁，β₂，···，β_m是n维欧氏空间V中两个向量组，证明存在一正交变换<img src='https://img2.soutiyun.com/ask/2021-01-07/978883779274006.jpg' />使<img src='https://img2.soutiyun.com/ask/2021-01-07/978883793368812.jpg' />的充分必要条件为<img src='https://img2.soutiyun.com/ask/2021-01-07/978883812679917.jpg' />

设e1,e2,...en,为内积空间X中规范正交系,证明:X到span{e1,e2,...en}的投影算子P为<img src='https://img2.soutiyun.com/ask/2020-08-13/966183831874337.png' /><img src='https://img2.soutiyun.com/shangxueba/ask/50580001-50583000/50580897/spacer.gif' />

证明不等式：<img src='https://img2.soutiyun.com/ask/2020-08-18/966606791867552.png' />

设n是大于零的整数，p为素数，证明<img src='https://img2.soutiyun.com/ask/2020-09-28/970161671001187.jpg' />

证明恒等式：<img src='https://img2.soutiyun.com/ask/2020-08-10/965923265077714.png' />

设A=[a_ij]为n阶实对称矩阵，λ₁≥λ₂≥...≥λ_n为其特征值，证明：<img src='https://img2.soutiyun.com/ask/2020-11-27/97534084251998.jpg' />