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 . 1/8 B . 3/8 C . 5/8 D . 7/8

A . e-1 B . e-2 C . -3 D . e-5

A .https://assets.asklib.com/psource/2015103009312036835.jpg B .https://assets.asklib.com/psource/201510300931322338.jpg C .https://assets.asklib.com/psource/2015103009314324351.jpg D .https://assets.asklib.com/psource/2015103009315762276.jpg

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

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' />

随机变量X服从正态分布，概率密度为<img src='https://img2.soutiyun.com/latex/latex.action' />，则k=______

A．<img src='https://img2.soutiyun.com/latex/latex.action' />B．<img src='https://img2.soutiyun.com/latex/latex.action' />C．4 D．5

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

A．A=-1，B=1 B．A=1，B=1 C．<img src='https://img2.soutiyun.com/ask/uploadfile/6663001-6666000/a314a24ce11f35ee3141709339fd2064.png' />D．A=B=-1

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' />

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' />

设给定两随机变量x₁和x₂，它们的联合概率密度为<img src='https://img2.soutiyun.com/ask/2020-10-16/971728750020193.png' />求随机变量<img src='https://img2.soutiyun.com/ask/2020-10-16/971728915910885.png' />的概率密度，并计算Y的熵h(Y)。

已知随机变量X的概率密度为<img src='https://img2.soutiyun.com/ask/2020-10-05/970734209803097.jpg' />,-∞＜x＜+∞,且随机变量Y=min(1,|X|),求EY.

(1)信源X的熵H_C(X); (2)Y= X+A(A＞0)的熵H_C(Y); (3)Y= 2X的熵H_C(Y)。

设随机变量(X，Y)的联合概率密度为 <img src='https://img2.soutiyun.com/ask/2020-12-28/978013315339139.jpg' /> (1)确定常数k； (2)求出X与Y的边缘概率密度； (3)判断X与Y是否相互独立； (4)求条件概率密度f_X|Y(x|y)，f_Y|X(y|x)。

设随机变量X的概率密度为<img src='https://img2.soutiyun.com/ask/2020-11-26/975236522008382.jpg' />，求下列随机变量函数的概率密度： (1)Y₁=2X; (2)Y₂=-X+1; (3)Y₃=X²。

设随机变量X的概率密度为<img src='https://img2.soutiyun.com/ask/2020-11-26/975238191352863.jpg' />已知EX=0.75，求k及a的值。

设随机变量X服从拉普拉斯分布，其概率密度为<img src='https://img2.soutiyun.com/ask/2020-08-09/965831888143643.png' />，其中1＞0为常数,求X的k阶中心矩。

A．1/2 B．1/3 C．1/4 D．1/5

设随机变量X的概率密度为<img src='https://img2.soutiyun.com/ask/2020-08-08/96574516377945.png' />。 问：X与|X|是否相互独立？

设二维随机变量(X，Y)的联合概率密度为<img src='https://img2.soutiyun.com/ask/2020-11-26/975236663523476.jpg' /> 求随机变量Z=X²+Y²的概率密度。