设，试求

图电路中，<img src='https://img2.soutiyun.com/latex/latex.action' />，试求反映有效值的电压表读数(设电压表的内阻为无限大)。 <img src='https://img2.soutiyun.com/ask/5499001-5502000/b8ff552107da3e5b8e5b4a052eb9688b.jpg' />

<img src='https://img2.soutiyun.com/ask/2021-01-21/980097424994737.jpg' />

设随机变量X的密度函数如下，试求E(2X+5). <img src='https://img2.soutiyun.com/ask/2020-08-03/965298880343798.png' />

<img src='https://img2.soutiyun.com/ask/2020-08-04/965404827120282.png' />

设一个信号s(t)可以表示成 <img src='https://img2.soutiyun.com/ask/2020-08-31/967711350043244.png' /> 试求:(1)信号的傅里叶级数的系数Cn;(2)信号的功率谱密度。

设曲线y=f(x)在原点与y=sinx相切,试求极限<img src='https://img2.soutiyun.com/ask/2020-08-18/9666107632147.png' />

设随机变量(X，Y)的联合密度函数为 <img src='https://img2.soutiyun.com/ask/2020-08-03/965319564212848.png' /> 试求E(Y/X).

设二维离散随机变量(X，Y)的联合分布列为 <img src='https://img2.soutiyun.com/ask/2020-08-03/965322644149011.png' /> 试求E(X|Y=2)和E(Y|X=0).

设3阶矩阵A与矩阵<img src='https://img2.soutiyun.com/ask/2020-12-21/977394217576874.png' />相似，试求矩阵A的特征值。

设f(x)具有连续的导函数，试求<img src='https://img2.soutiyun.com/ask/2021-01-13/979407729470513.jpg' />

设x₁，…，x_n是来自U(-1，1)的样本，试求<img src='https://img2.soutiyun.com/ask/2020-08-04/965388678148613.png' />

设X与Y相互独立，它们的分布律为<img src='https://img2.soutiyun.com/ask/2020-11-25/97514825505304.jpg' />试求X+Y的分布律。

<img src='https://img2.soutiyun.com/ask/2020-06-28/962202187481013.png' />

<img src='https://img2.soutiyun.com/ask/2020-08-12/96609905828463.png' />

设(X, Y)服从以原点为圆心的单位圆上的均匀分布，记<img src='https://img2.soutiyun.com/ask/2020-09-29/970261341095668.png' />.试求(U, V)的联合分布律.

<img src='https://img2.soutiyun.com/ask/2020-11-06/97352995306369.jpg' />

<img src='https://img2.soutiyun.com/ask/2021-01-04/978627879674219.png' />